Big Data and the Web: Algorithms for Data Intensive Scalable Computing
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This document is the dissertation of Gianmarco De Francisci Morales submitted for the PhD program in Computer Science and Engineering at IMT Institute for Advanced Studies in Lucca, Italy. The dissertation addresses challenges in managing and analyzing large datasets, or "big data", and presents algorithms for tasks like document filtering, graph computation and real-time news recommendation. It was approved by the program coordinator and supervisor, and reviewed by two external reviewers. The dissertation contains six chapters, including introductions to big data and related work, and presents three contributed algorithms for document filtering, graph computation and news recommendation that scale to large datasets through parallel and distributed techniques.
![ate key with all its associated values to produce the final result. The two
phases are strictly non overlapping. The general signatures of the two
phases of a MapReduce computation are as follows:
Map: k1, v1 → [ k2, v2 ]
Reduce: k2, [v2] → [ k3, v3 ]
The Map and Reduce function are purely functional and thus without
side effects. This property makes them easily parallelizable because each
input key-value is independent from the other ones. Fault tolerance is
also easily achieved by just re-executing the failed function instance.
MapReduce assumes a distributed file systems from which the Map
instances retrieve their input data. The framework takes care of mov-
ing, grouping and sorting the intermediate data produced by the various
mappers (tasks that execute the Map function) to the corresponding re-
ducers (tasks that execute the Reduce function) .
The programming interface is easy to use and does not require any
explicit control of parallelism. A MapReduce program is completely de-
fined by the two UDFs run by mappers and reducers. Even though the
paradigm is not general purpose, many interesting algorithms can be
implemented on it. The most paradigmatic application is building an in-
verted index for a Web search engine. Simplistically, the algorithm reads
the crawled and filtered web documents from the file system, and for
every word it emits the pair word, doc_id in the Map phase. The Re-
duce phase simply groups all the document identifiers associated with
the same word word, [doc_id1, doc_id2, . . .] to create an inverted list.
The MapReduce data flow is illustrated in Figure 2.2. The mappers
read their data from the distributed file system. The file system is nor-
mally co-located with the computing system so that most reads are local.
Each mapper reads a split of the input, applies the Map function to the
key-value pair and potentially produces one or more output pairs. Map-
pers sort and write intermediate values on the local disk.
Each reducer in turn pulls the data from various remote locations.
Intermediate key-value pairs are already partitioned and sorted by key
by the mappers, so the reducer just merge-sorts the different partitions to
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![The model makes a number of assumptions on the underlying infras-
tructure to derive the definition. The number of available processors is
assumed to be sub-linear. This restriction guarantees that algorithms in
MRC are practical. Each processor has a sub-linear amount of memory.
Given that the Reduce phase can not begin until all the Maps are done,
the intermediate results must be stored temporarily in memory. This
explains the space limit on the Map output which is given by the total
memory available across all the machines. The authors give examples of
algorithms for graph and string problems. The result of their analysis is
an algorithmic design technique for MRC.
A number of extensions to the base MR system have been developed.
Many of these works focus on extending MR towards the database area.
Yang et al. (2007) propose an extension to MR in order to simplify the
implementation of relational operators. More specifically they target the
implementation of join, complex, multi-table select and set operations.
The normal MR workflow is extended with a third final Merge phase.
This function takes as input two different key-value pair lists and outputs
a third key-value pair list. The model assumes that the output of the
Reduce function is fed to the Merge. The signature are as follows.
Map: k1, v1 α → [ k2, v2 ]α
Reduce: k2, [v2] α → k2, [v3] α
Merge: k2, [v3] α , k3, [v4] β → [ k4, v5 ]γ
where α, β, γ represent data lineages. The lineage is used to distinguish
the source of the data, a necessary feature for joins.
The signatures for the Reduce function in this extension is slightly
different from the one in traditional MR. The Merge function requires its
input to be organized in partitions. For this reason the Reduce function
passes along the key k2 received from the Map to the next phase without
modifying it. The presence of k2 guarantees that the two inputs of the
Merge function can be matched by key.
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![3.2 Problem definition and preliminaries
We address the similarity self-join problem applied to a collection D of
documents. Let L be the lexicon of the collection. Each document d is
represented as a |L|-dimensional vector. Without loss of generality, we
assume that documents are normalized, so d[i] denotes the number of
occurrences of the i-th term in the document d divided by the norm d .
We adopt the cosine distance to measure the similarity between two doc-
uments. For normalized documents the cosine similarity can be simply
computed as the inner product between document vectors.
Problem 1 (Similarity Self-Join Problem). Given a collection of normalized
document-vectors D = {d1, . . . , dN }, a similarity function σ: D×D → R and
a minimum similarity threshold σ, the Similarity Self-Join problem requires to
discover all those pairs di, dj ∈ D with similarity above the threshold:
σ(di, dj) =
0≤t<|L|
di[t] · dj[t] ≥ σ
Note that the results discussed in this chapter can be easily applied to
other similarity measures, such as Jaccard, Dice or overlap.
Differently from normal join problems, self-join involves joining a
large table with itself. Thus it is not possible to apply traditional algo-
rithms for data warehousing, that join a large fact table with smaller di-
mension tables. Recent algorithms for log processing in MR also assume
that one of the tables is much smaller that the other (Blanas et al., 2010).
Following Arasu et al. (2006); Xiao et al. (2009), we classify algorithms
for similarity self-join by their solution to the following sub-problems:
1. Signature scheme: a compact representation of each document;
2. Candidate generation: identifying potentially similar document
pairs given their signature;
3. Verification: computing document similarity;
4. Indexing: data structures for speeding up candidate generation
and verification.
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![The naïve approach produces the document itself as the signature.
It generates all the O(N2
) possible document-signature pairs, and com-
putes their actual similarity without any supporting indexing structure.
This approach is overly expensive in the presence of sparse data such
as bag of documents. It is very common to have documents thad to not
share any term, leading to a similarity of zero. In this case, smart pruning
strategies can be exploited to discard early such document pairs.
Broder et al. (1997) adopt a simple signature scheme, that we refer
to as Term-Filtering. The signature of a document is given by the terms
occurring in that document. These signatures are stored in an inverted
index, which is then used to compare only pairs of documents sharing at
least one item in their signature, i.e. one term.
Prefix-Filtering (Chaudhuri et al., 2006) is an extension of the Term-
Filtering idea. Let ˆd be an artificial document such that ˆd[t] = maxd∈D d[t].
Given a document d, let its boundary b(d) be the largest integer such that
0≤t<b(d) d[t] · ˆd[t] < σ. The signature of the document d is the set of
terms occurring in the document vector beginning from position b(d),
S(d) = {b(d) ≤ t < |L| | d[t] = 0}. It is easy to show that if the signatures
of two documents di, dj have empty intersection, then the two docu-
ments have similarity below the threshold. Without loss of generality let
us assume that b(di) b(dj).
(S(di) ∩ S(dj) = ∅) ⇒
b(di)≤t<|L|
di[t] · dj[t] = 0 ⇒
σ(di, dj) =
0≤t<b(di)
di[t] · dj[t] ≤
0≤t<b(di)
di[t] · ˆd[t] < σ
Therefore, only document signatures are stored in the inverted index
and later used to generate candidate document pairs. Eventually, the full
documents need to be retrieved in order to compute the actual similarity.
This technique was initially proposed for set-similarity joins and later
extended to documents with real-valued vectors.
In particular, Bayardo et al. (2007) adopt an online indexing and match-
ing approach. Index generation, candidate pair generation and similarity
score computation are all performed simultaneously and incrementally.
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![Each document is matched against the current index to find potential
candidates. The similarity scores are computed by retrieving the candi-
date documents directly from the collection. Finally, a signature is ex-
tracted from the current document and added to the index.
This approach results in a single full scan of the input data, a small
number of random accesses to single documents, and a smaller (on av-
erage) index to be queried. Prefix-filtering outperforms alternative tech-
niques such as LSH (Gionis et al., 1999), PartEnum (Arasu et al., 2006)
and ProbeCount-Sort (Sarawagi and Kirpal, 2004), which we therefore
do not considered in our work. Unfortunately, an incremental approach
that leverages a global shared index is not practical on a large parallel
system because of contention on the shared resource.
Finally, Xiao et al. (2008) present some additional pruning techniques
based on positional and suffix information. However these techniques
are specifically tailored for set-similarity joins and cannot be directly ap-
plied to document similarity.
3.3 Related work
In this section we describe two MR algorithm for the similarity self-join
problem. Each exploits one of the pruning techniques discussed above.
3.3.1 MapReduce Term-Filtering (ELSA)
Elsayed et al. (2008) present a MapReduce implementation of the Term-
Filtering method. Hereafter we refer to it as ELSA for convenience. The
authors propose an algorithm for computing the similarity of every doc-
ument pair, which can be easily adapted to our setting by adding a sim-
ple post-filtering. The algorithm runs two consecutive MR jobs, the first
builds an inverted index and the second computes the similarities.
Indexing: Given a document di, for each term, the mapper emits the term
as the key, and a tuple i, di[t] consisting of document ID and weight as
the value. The shuffle phase of MR groups these tuples by term and
delivers these inverted lists to the reducers, that write them to disk.
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![Map: i, di → [ t, i, di[t] | di[t] > 0]
Reduce: t, [ i, di[t] , j, dj[t] , . . .] → [ t, [ i, di[t] , j, dj[t] , . . .] ]
Similarity: Given the inverted list of term t, the mapper produces the
contribution wij[t] = di[t] · dj[t] for every pair of documents where the
term t co-occurs. This value is associated with a key consisting of the pair
of document IDs i, j . For any document pair the shuffle phase will pass
to the reducer the contribution list Wij = {wij[t] | wij[t] > 0, ∀t ∈ L}
from the various terms, which simply need to be summed up.
Map: t, [ i, di[t] , j, dj[t] , . . .] → [ i, j , wij[t] ]
Reduce: i, j , Wij →
i, j , σ(di, dj) =
w∈Wij
w
The Term-Filtering is exploited implicitly: the similarity of two doc-
uments that do not share any term is never evaluated because none of
their terms ever occurs in the same inverted list.
The main drawback of this approach is caused by the large number
of candidate document pairs that it generates. In fact, there are many
document pairs that share only a few terms but have anyway a simi-
larity largely below the threshold. The number of candidates directly
affects completion time. More importantly it determines the shuffle size,
the volume of intermediate data to be moved from mappers to reducers.
Minimizing shuffle size is critical because network bandwidth is the only
resource that cannot be easily added to a cluster.
Finally, recall that reducers may start only after every mapper has
completed. Therefore, the presence of a few long inverted lists for com-
mon terms induces a significant load imbalance. Most of the resources
will remain idle until the processing of the longest inverted list is com-
pleted. To alleviate this issue Elsayed et al. remove the top 1% most fre-
quent terms, thus trading efficiency for precision. Our goal is to provide
an efficient algorithm that computes the exact similarity.
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![Figure 3.1 illustrates an example of how ELSA works. For ease of
explanation, the document vectors are not normalized. Term-Filtering
avoids computing similarity scores of documents that do not share any
term. For the special case in which an inverted list contains only one doc-
ument, the similarity Map function does not produce any output. The
two main problems of ELSA result evident from looking at this image.
First, long inverted lists may produce a load imbalance and slow down
the algorithm considerably, as for term “B” in the figure. Second, the
algorithm computes low similarity scores which are not useful for the
typical applications, as for document pair d1, d2 in the figure.
shuffle
map
map
map
map
shuffle
<B, [(d1,1),
(d2,1),
(d3,2)]>
<C, [(d1,1),
(d3,1)]>
<D, [(d2,2)]>
<A, [(d1,2),
(d3,1)]>
<A, (d1,2)>
<B, (d1,1)>
<C, (d1,1)>
<B, (d2,1)>
<D, (d2,2)>
<A, (d3,1)>
<B, (d3,2)>
<C, (d3,1)>
<B, [(d1,1),
(d2,1),
(d3,2)]>
<A, [(d1,2),
(d3,1)]>
<C, [(d1,1),
(d3,1)]>
<D, [(d2,2)]>
reduce
reduce
reduce
reduce
Indexing Similarity
<(d1,d2), 1>
<(d1,d3), 2>
<(d2,d3), 2>
<(d1,d3), 1>
<(d1,d3), 2>
<(d1,d3), [2,2,1]>
<(d1,d2), [1]>
<(d2,d3), [2]>
reduce
reduce
reduce
<(d1,d3), 5>
<(d1,d2), 1>
<(d2,d3), 2>
mapd1
"A A B C"
mapd3
"A B B C"
mapd2
"B D D"
Figure 3.1: ELSA example.
3.3.2 MapReduce Prefix-Filtering (VERN)
Vernica et al. (2010) present a MapReduce algorithm based on Prefix-
Filtering that uses only one MR step. Indeed, the authors discuss several
algorithm for set-similarity join operations. Here we describe the best
performing variant for set-similarity self-join. Hereafter we refer to it as
VERN for convenience. For each term in the signature of a document
t ∈ S(di) as defined by Prefix-Filtering, the map function outputs a tuple
with key the term t itself and value the whole document di. The shuffle
phase delivers to each reducer a small sub-collection of documents that
share at least one term in their signatures. This process can be thought
as the creation of an inverted index of the signatures, where each post-
ing is the document itself rather than a simple ID. Finally, each reducer
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![finds similar pairs among candidates by using state-of-the-art serial algo-
rithms (Xiao et al., 2008). The Map and Reduce functions are as follows.
Map: i, di → [ t, di | t ∈ S(di)]
Reduce: t, Dv = [di, dj, . . .] → [ i, j , σ(di, dj) | di, dj ∈ Dv]
Nonetheless, this approach does not bring a significant improvement
over the previous strategy. First, a document with a signature of length
n is replicated n times, even if there are no other documents with an
overlapping signature. Second, pairs of similar documents that have m
common terms in their signatures are produced m times at different re-
ducers. Computing these duplicates is a overhead of parallelization, and
their presence requires a second scan of the output to get rid of them.
Figure 3.2 illustrates an example run of VERN. Light gray terms are
pruned from the document by using Prefix-Filtering. Each document is
replicated once for each non-pruned term it contains. Finally, the reducer
computes the similarity of the bag of documents it receives by employ-
ing a serial SSJ algorithm. As shown in Figure 3.2, VERN computes the
similarity of the pair d1, d3 multiple times at different reducers.
We propose here a simple strategy that solves the issue of duplicate
similarity computation. We use this modified version of the original
VERN algorithm in our evaluation. This modified version runs slightly
but consistently faster than the original one, and it does not require post-
processing. The duplicate similarities come from pair of documents that
share more than one term in their signatures. Let Sij = S(di) ∩ S(dj)
be the set of such shared terms in document pair di, dj . Let ˆt be the
last of such terms in the order imposed to the lexicon by Prefix-Filtering
ˆt = tx | tx ty ∀ tx, ty ∈ Sij. The reducer that receives each pair can
simply check if its key corresponds to ˆt and compute the similarity only
in this case. The term ˆt for each pair of documents can be efficiently com-
puted by a simple backwards scan of the two arrays that represent the
documents. This strategy allows to avoid computing duplicate similari-
ties and does not impose any additional overhead the original algorithm.
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![shuffle
<(d1,d3), 5>
<(d1,d3), 5>
<A, (d1, A A B C)>
<B, (d1, A A B C)>
<C, (d1, A A B C)>
<D, (d2, B D D)>
<B, (d3, A B B C)>
<C, (d3, A B B C)>
mapd1
"A A B C"
mapd2
"B D D"
mapd3
"A B B C"
<B, [(d1, A A B C),
(d3, A B B C)]>
<A, (d1, A A B C)>
<C, [(d1, A A B C),
(d3, A B B C)]>
<D, [(d2, B D D)]>
reduce
reduce
reduce
reduce
Figure 3.2: VERN example.
3.4 SSJ Algorithms
In this section we describe two algorithms based on Prefix-Filtering that
overcome the weak points of the algorithms presented above. The first
algorithm, named SSJ-2, performs a Prefix-Filtering in two MR steps.
Note that in the first step we use a naïve indexing algorithm but if needed
more advanced techniques can be used (McCreadie et al., 2009b, 2011).
The second algorithm, named SSJ-2R, additionally uses a remainder file
to broadcast data that is likely to be used by every reducer. It also effec-
tively partitions the search space to reduce the memory footprint. Code
for both algorithm is open source and available online.2
3.4.1 Double-Pass MapReduce Prefix-Filtering (SSJ-2)
This algorithm is and extention of ELSA, and also consists of an indexing
phase followed by a similarity computation phase.
SSJ-2 shortens the inverted lists by employing Prefix-Filtering. As
shown in Figure 3.3, the effect of Prefix-Filtering is to reduce the portion
of document indexed. The terms occurring in di up to position b(di), or
bi for short, need not be indexed. By sorting terms in decreasing order of
frequency, the most frequent terms are discarded. This pruning shortens
the longest inverted lists and brings a significant performance gain.
2https://github.com/azaroth/Similarity-Self-Join
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![of documents is sent to the reducer only if they share at least one term
in their signature. Furthermore, while SSJ-2 computes the similarity be-
tween any two given documents just once, VERN computes the similarity
of two documents in as many reducers as the size of the intersection of
their signatures. Therefore, SSJ-2 has no computational overhead due to
parallelization, and significantly reduces communication costs.
Figure 3.4 presents an example for SSJ-2. As before, light gray terms
have been pruned and documents are not normalized to ease the expla-
nation. Pairs of documents that are below the similarity threshold are
discarded early. However the reducer of the similarity phase needs to
access the remote file system to retrieve the documents in order to com-
pute the correct final similarity score.
shuffle
<(d1,d3), 2>
<(d1,d3), 1>
<(d1,d3), [2,1]> reduce <(d1,d3), 5>
HDFS
d3
"A B B C"
d1
"A A B C"
Similarity
map
map
map
shuffle
<B, [(d1,1),
(d3,2)]>
<C, [(d1,1),
(d3,1)]>
<D, [(d2,2)]>
<B, (d1,1)>
<C, (d1,1)>
<D, (d2,2)>
<B, (d3,2)>
<C, (d3,1)>
mapd1
"A A B C"
mapd2
"B D D"
mapd3
"A B B C"
<B, [(d1,1),
(d3,2)]>
<C, [(d1,1),
(d3,1)]>
<D, [(d2,2)]>
reduce
reduce
reduce
Indexing
Figure 3.4: SSJ-2 example.
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![3.4.2 Double-Pass MapReduce Prefix-Filtering with Re-
mainder File (SSJ-2R)
For any given pair of documents di, dj , the reducers of SSJ-2 receive
only partial information. Therefore, they need to retrieve the full docu-
ments in order to correctly compute their similarity. Since a node runs
multiple reducers over time, each of them remotely accessing two doc-
uments, in the worst case this is equivalent to broadcasting the full col-
lection to every node, with obvious limitations to the scalability of the
algorithm. We thus propose an improved algorithm named SSJ-2R that
does not perform any remote random access, and that leverages the non-
indexed portion of the documents.
Let us make a few interesting observations. First, some of the terms
are very common, and therefore used to compute the similarity of most
document pairs. For those terms, it would be more efficient to broad-
cast their contributions rather than pushing them through the MR frame-
work. Indeed, such piece of information is the one pruned via Prefix-
Filtering during the indexing phase. We thus propose to store the pruned
portion of each document in a remainder file DR, which can be later re-
trieved by each reducer from the underlying distributed file system.
Second, the remainder file DR does not contain all the information
needed to compute the final similarity. Consider Figure 3.3, each reducer
receives the contributions wij[t] = di[t] · dj[t] | t bj. DR contains in-
formation about the terms di[t] | t bi} and {dj[t] | t bj. But, subtly,
no information is available for those terms di[t] | bi t bj. On the
one hand, those term weights are not in the remainder file because they
have been indexed. On the other hand, the corresponding inverted lists
contain the frequency of the terms in di but not of those occurring in dj,
and therefore, the weights wij[t] = di[t] · dj[t] cannot be produced.
We thus propose to let one of the two documents be delivered to
the reducer through the MR framework by shuffling it together with the
weights of the document pairs. Given two documents di and dj as shown
in Figure 3.3, if bi bj we call di the Least Pruned Document and dj the
Most Pruned Document. Our goal is to group at the reducer each docu-
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![ment d with the contributions w of every document pair di, dj for which
d is the least pruned document between di and dj. This document con-
tains the pieces of information that we are missing in order to compute
the final similarity score. This can be achieved by properly defining the
keys produced by the mappers and their sorting and grouping operators.
More formally, we define two functions LPD(di, dj) and MPD(di, dj).
LPD(di, dj) =
i, if bi bj
j, otherwise
MPD(di, dj) =
j, if bi bj
i, otherwise
First, we slightly modify the similarity Map function such that for ev-
ery document pair of the given inverted list, it produces as keys a couple
of document IDs where the first is always the LPD, and as values the
MPD and the usual weight w.
Map: [ t, [ i, di[t] , j, dj[t] , . . .] ] →
[ LPD(di, dj), MPD(di, dj) , MPD(di, dj), wij[t] ]
Second, we take advantage of the possibility of running independent
Map functions whose outputs are then shuffled together. We define a
Map function that takes the input collection and outputs its documents.
Map: i, di → [ i, φ , di ]
where φ is a special value such that φ < i ∀di ∈ D.
Third, we make use of the possibility offered by Hadoop to rede-
fine parts of its communication pattern. The process we describe here
is commonly known as secondary sort in MR parlance. We redefine the
key partitioning function, which selects which reducer will process the
key. Our function takes into account only the first document ID in the
key. This partitioning scheme guarantees that all the key-value pairs that
share the same LPD will end up in the same partition, together with one
copy of the LPD document itself coming from the second Map function.
We instruct the shuffle phase of MR to sort the keys in each partition
in ascending order. This order takes into account both IDs, the first as
primary key and the second as secondary key. Consequently, for each
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![document di MR builds a list of key-value pairs such that the first key is
i, φ , followed by every pair of document IDs for which di is the LPD.
Finally, we override the grouping function, which determines whether
two keys belong to the same equivalence class. If two keys are equiva-
lent, their associated values will be processed by the same single call to
the Reduce function. Concretely, the grouping function builds the argu-
ment list for a call to the Reduce function by selecting values from the
partition such that the corresponding keys are equivalent. Therefore our
grouping function must consistent with our partitioning scheme: two
keys i, j and i , j are equivalent iff i = i .
The input of the Reduce function is thus as follows.
i, φ , [di, j, wij[t ] , j, wij[t ] , . . . , k, wik[t ] , k, wik[t ] , . . .]
The key is just the first key in the group, as they are all equivalent to
MR. The first value is the LPD document di. Thanks to the sorting of the
keys, it is followed by a set of contiguous stripes of weights. Each stripe
is associated to the same document dj | j = MPD(di, dj).
SSJ-2R can now compute the similarity σ(di, dj) in one pass. Before
the algorithm starts, each reducer loads the remainder file DR in mem-
ory. For each Reduce call, SSJ-2R starts by caching di, which is at the
beginning of the list of values. Then, for each dj in the list, it sums up all
the corresponding weights wij to compute a partial similarity. Finally, it
retrieves the pruned portion of dj from DR, computes the similarity of
di to the pruned portion of dj and adds this to the partial similarity com-
puted before. This two step process correctly computes the final similar-
ity σ(di, dj) because all the terms bi t bj are available both in di and
in the pruned portion of dj. This process is repeated for each stripe of
weights belonging to the same document pair in the list of values.
Differently from SSJ-2, SSJ-2R performs no remote access to the doc-
ument collection. Given a document pair, one is delivered fully through
the MapReduce framework, and the other is partially retrieved from the
remainder file DR. The advantage in terms of communication costs is
given by the remainder file. Indeed, DR is much smaller than the input
collection. We show experimentally that its size is one order of magni-
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![shuffle
<B, [(d1,1),
(d3,2)]>
<C, [(d1,1),
(d3,1)]>
<D, [(d2,2)]>
<B, (d1,1)>
<C, (d1,1)>
<D, (d2,2)>
<B, (d3,2)>
<C, (d3,1)>
mapd1
"A A B C"
mapd2
"B D D"
mapd3
"A B B C"
<B, [(d1,1),
(d3,2)]>
<C, [(d1,1),
(d3,1)]>
<D, [(d2,2)]>
reduce
reduce
reduce
Indexing
shuffle
<(d1,d3), 2>
<(d1,d3), 1>
<(d1,✦),"A A B C">
<(d1,d3), 2>
<(d1,d3), 1>
reduce <(d1,d3), 5>
Similarity
map
map
map
map
Remainder
File
d1 "A A"
d3 "A"
d2 "B"
Distributed Cache
<(d1,✦),
"A A B C">
<(d3,✦),
"A B B C">
Figure 3.5: SSJ-2R example.
di at each of these reducers. For this reason, we replicate K times the
special key i, φ and its associated value di, once for each partition.
The parameter K allows to tune the memory usage of SSJ-2R and
controls the tradeoff with the communication cost due to replication.
3.5 Complexity analysis
In Section 2.2.1 we presented a few proposals for modeling MapReduce
algorithms (Afrati and Ullman, 2009; Karloff et al., 2010). Indeed, esti-
mating the cost of a MapReduce algorithm is quite difficult, because of
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![4.5.2 The STACKMR algorithm
Our first matching algorithm, STACKMR, is a variant of the algorithm
developed by Panconesi and Sozio (2010). Panconesi and Sozio propose
a complex mechanism to ensure that capacity constraints are satisfied,
which unfortunately does not seem to have an efficient implementation
in MapReduce. Here we devise a more practical variant that allows node
capacities to be violated by a factor of at most (1 + ), for any > 0. This
approximation is a small price to pay in our application scenarios, where
small capacity violations can be tolerated.
For the sake of presentation, we describe our algorithm first in a cen-
tralized environment and then in a parallel environment. Pseudocode
for STACKMR and for the algorithm by Panconesi and Sozio are shown
in Algorithms 1 and 2, respectively.
The latter one has been slightly changed so to take into account im-
plementation issues. However, we do not include an evaluation of the
latter algorithm as it does not seem to be efficient. In the next section we
describe in detail how to implement the former algorithm in MapReduce.
Our algorithm is based on the primal-dual schema, a successful and
established technique to develop approximation algorithms. The primal-
dual schema has proved to play an important role in the design of se-
quential and distributed approximation algorithms. We hold the belief
that primal-dual algorithms bear the potential of playing an important
role in the design of MapReduce algorithms as well.
The first step of any primal-dual algorithm is to formulate the prob-
lem at hand as an integer linear program (IP). Each element that might
be included in a solution is associated with a 0-1 variable. The combina-
torial structure of the problem is captured by an objective function and a
set of constraints, both being a linear combination of the binary variables.
Then, integrality constraints are relaxed so that variables can take any
value in the range [0, 1]. This linear program is called primal. From the
primal program we derive the so-called dual. There is a direct correspon-
dence between the variables of the primal and the constraints of the dual,
as well as, the variables of the dual and the constraints of the primal.
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![communication rounds, with high probability.
The non-determinism follows from the algorithm that computes max-
imal b-matchings. The proof of Theorem 1 is similar to the one given
by Panconesi and Sozio. STACKMR is a factor 1/ faster than the original.
4.5.3 Adaptation in MapReduce
The distributed algorithm described in the previous section works in an
iterative fashion. In each iteration we first compute a maximal matching,
then we push it on a stack, we update edges, and we pop all levels from the
stack. Below we describe how to implement these steps in MapReduce.
Maximal matching. To find maximal b-matchings we employ the al-
gorithm of Garrido et al. which is an iterative probabilistic algorithm.
Each iteration consists of four stages: (i) marking, (ii) selection, (iii)
matching, and (iv) cleanup.
In the marking stage, each node v marks randomly 1
2 b(v) of its
incident edges. In the selection stage, each node v selects randomly
max{ 1
2 b(v) , 1} edges from those marked by its neighbors. Call F this
set of selected edges. In the matching stage, if some node v has ca-
pacity b(v) = 1 and two incident edges in F, it randomly deletes one of
them. At this point the set F is a valid b-matching. The set F is added
to the solution and removed from the original graph. In the cleanup
stage, each node updates its capacity in order to take into consideration
the edges in F and saturated nodes are removed from the graph. These
stages are iterated until there are no more edges left in the original graph.
The process requires, on expectation, O(log3
n) iterations to terminate.
To adapt this algorithm in MapReduce, we need one job for each stage
of the algorithm. The input and output of each MapReduce job is al-
ways of the same format: a consistent view of the graph represented as
adjacency lists. We maintain a node-based representation of the graph
because we need to make decisions based on the local neighborhood of
each node. Assuming the set of nodes adjacent to vi is {vj, . . . , vk}, the
input and output of each job is a list of pairs vi, [(vj, Tij), . . . , (vk, Tik)] ,
where vi is the key and [(vj, Tj), . . . , (vk, Tk)] the associated value. The
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![variables T represent the state of each edge. We consider five possible
states of an edge: E in the main graph; K marked; F selected; D deleted;
and M in the matching. The 4 stages of the algorithm are repeated until
all the edges are in the matching (M) or are deleted (D).
The general signature of each job is as follows.
Map: vi, [(vj, Tij), . . . , (vk, Tik)] →
vi, T
(i)
ij , vj, T
(i)
ij , . . . , vi, T
(i)
ik , vk, T
(i)
ik
Reduce: vi, T
(i)
ij , vi, T
(j)
ij , . . . , vi, T
(i)
ik , vk, T
(k)
ik →
vi, [(vj, Tij), . . . , (vk, Tik)]
where T
(i)
ij is the state of edge (vi, vj) as locally viewed by vi and Tij is
the final state after unification of the views from vi and vj.
Each Map function alters the state of the graph locally to each node.
Each Reduce function unifies the diverging views of the graph at each
node. For each edge (vi, vj), each Map function will emit both vi and vj
as keys, together with the current state of the edge as value. The Reduce
function will receive the views of the state of the edge from both end-
points, and will unify them, yielding a consistent graph representation.
Unification is performed by a simple precedence rule. If a b the algo-
rithm unifies two diverging states (a, b) to state b. Only a subset of all
the possible combinations of states may actually happen, so we need to
specify only a few rules as follows.
E K F; F M; E D;
Each MapReduce job uses the same communication pattern and state
unification rules. They only differ in the way they update the state of
the edges. The communication cost of each job is thus O(|E|), while the
achievable degree of parallelism is O(|V |). Figure 4.2 illustrates the com-
munication pattern, which is the same for each vertex. Let us take into
account the central node. For each incident edge, the mapper emits the
edge state as viewed by the node twice: once for each end of the edge.
In the picture the state view is represented by the arrows which are color
coded to represent their origin and point to their destination. For each
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![threshold into Equation (5.2) as follows:
Rc(ni)(u, ni) > Rc(ni)(u, nj) + 1 − ξijc(ni)
for all nj ∈ N [c(ni) − τ, c(ni)] , (5.3)
where N [c(ni) − τ, c(ni)] is the set of news articles published between
time c(ni) − τ and c(ni).
Finally, we further restrict N [c(ni) − τ, c(ni)] by considering only the
articles which that are relevant according to at least one of the three score
components Στ , Γτ , Πτ . Let Top(k, χ, τa, τb) be the set of k news articles
with largest rank in the set N [τa, τb] according to the score component χ.
We include into the optimization Problem 4 only the constraints:
Rc(ni)(u, ni) > Rc(ni)(u, nj) + 1 − ξijc(ni)
for all nj s.t. nj ∈ Top k, Σc(ni), c(ni) − τ, c(ni) or
nj ∈ Top k, Γc(ni), c(ni) − τ, c(ni) or
nj ∈ Top k, Πc(ni), c(ni) − τ, c(ni) . (5.4)
By setting k = 10 we are able to reduce the number of constraints from
more than 25 million to approximately 250 thousand, thus significantly
reducing the training time of the learning algorithm.
5.5.2 Additional features
The system obtained by learning the model parameters using the SVM-
Rank method is named T.REX, and forms our main recommender. Ad-
ditionally, we attempt to improve the accuracy of T.REX by incorporat-
ing more features. To build this improved recommender we use exactly
the same learning framework: we collect more features from the same
training dataset and we learn their importance using the SVM-Rank al-
gorithm. We choose three additional features: age, hotness and click count,
which we describe below.
The age of a news article n is the time elapsed between the current
time and the time n was published, that is, τ − τ(n).
The hotness of a news article is a set of features extracted from the
vectors HT and HN , which keep the popularity counts for the entities in
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![cannot be automated, and they are impractical if more than one strategy
or many parameters need to be tested.
For these reasons, we propose an automated method to evaluate our
recommendation algorithm. The proposed evaluation method exploits
the available click data collected by the Yahoo! toolbar, and it is similar
in spirit with the learning process. Given a stream of news and a stream
of tweets for the user, we identify an event that a user clicks at a news
article n∗. Assume that such a click occurs at time τ = c(n∗). Suppose
the user just logged in the system at time τ. Then the recommendation
strategy should rank the news article n∗ as high as possible.
To create a test instance, we collect all news articles that have been
published within the time interval [τ − τ∗
, τ], and select a subset as de-
scribed by Equation (5.4): we pick the news with largest scores according
to the components of content, social, popularity, and number of clicks un-
til time τ. In total we generate a pool of k = 1,000 candidate news. All
these news articles are ranked using our ranking function Rτ , and we
then examine what is the ranking of the article n∗ in the list.
We use the last 20%, in chronological order, of the Yahoo! toolbar log
to test the T.REX and T.REX+ algorithms, as well as all the baselines.
5.6.3 Evaluation measures
Evaluating a ranking of items is a standard problem in information re-
trieval. In our setting we have only one correct answer per ranking —
the news article n∗ clicked by the user — and we care about the position
of this item in the ranking, which we evaluate using the Mean Reciprocal
Rank (MRR) measure Voorhees (1999):
MRR =
1
|Q|
Q
i=1
1
r(ni
∗)
,
where r(ni
∗) is the rank of the news article ni
∗ in the i-th event of the eval-
uation and Q is the set of all tests. The MRR measure is commonly used
to evaluate question-answering systems, where only the first correct an-
swer matters. MRR gives higher scores to correct results that are higher
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![in the ranking and reduces the importance of correct predictions in the
lower parts of the ranking.
We also compute the precision of our system at different levels. For
our task we define the precision-at-k (P@k) as the fraction of rankings in
which the clicked news is ranked in the top-k positions. We compute
P@k for k = 1, 5, and 10.
There are cases in which the sparsity of the data prevents our system
from providing recommendations. Therefore, we also evaluate the cov-
erage of our recommendations. We define the coverage as the fraction of
clicks for which we were able to provide some recommendation.
Finally, we note that when the user clicks on a news, the user is ac-
tually expressing interest in the entities mentioned in the news. We can
argue that if a user clicks on a report on Fukushima from CNN, the user
might equally be interested in a report on the same topic from BBC. In
this case, we would like to predict the entities that the user is interested
in, rather than the news articles themselves.
We use Jaccard overlap between the sets of entities mentioned in two
news articles to measure the similarity between the articles themselves.
We compute the similarity between each news article in the ranking and
the clicked news. Then, we assign a relevance level to each news by bin-
ning the computed similarity into five levels. This gives rise to a ranking
task with multiple levels of relevance. We use Discounted Cumulated
Gain (DCG) (Järvelin and Kekäläinen, 2002) to measure the performance
of the strategies on this newly defined task:
DCG [i] =
G [i] if i = 1;
DCG [i − 1] + G[i]
log2i if i > 1,
where G[i] is the relevance of the document at position i in our ranking.
We compute the DCG for the top 20 results averaged over all the rank-
ings produced. If a strategy is not able to produce a ranking, we pad the
ranking with non-relevant documents.
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Big Data and the Web: Algorithms for Data Intensive Scalable Computing
- 1. IMT Institute for Advanced Studies Lucca, Italy Big Data and the Web: Algorithms for Data Intensive Scalable Computing PhD Program in Computer Science and Engineering XXIV Cycle By Gianmarco De Francisci Morales 2012
- 3. The dissertation of Gianmarco De Francisci Morales is approved. Program Coordinator: Prof. Rocco De Nicola, IMT Lucca Supervisor: Dott. Claudio Lucchese, ISTI-CNR Pisa Co-Supervisor: Dott. Ranieri Baraglia, ISTI-CNR Pisa Tutor: Dott. Leonardo Badia, University of Padova The dissertation of Gianmarco De Francisci Morales has been reviewed by: Aristides Gionis, Yahoo! Research Barcelona Iadh Ounis, University of Glasgow IMT Institute for Advanced Studies, Lucca 2012
- 5. Where is the wisdom we have lost in knowledge? Where is the knowledge we have lost in information?
- 7. To my mother, for her unconditional love and support throughout all these years.
- 9. Acknowledgements I owe my deepest and earnest gratitude to my supervisor, Claudio Lucchese, who shepherded me towards this goal with great wisdom and everlasting patience. I am grateful to all my co-authors, without whom this work would have been impossible. A separate acknowledgement goes to Aris Gionis for his precious advice, constant presence and exemplary guidance. I thank all the friends and colleagues in Lucca with whom I shared the experience of being a Ph.D. student, my Lab in Pisa that accompanied me through this journey, and all the people in Barcelona that helped me feel like at home. Thanks to my family and to everyone who believed in me. ix
- 10. Contents List of Figures xiii List of Tables xv Publications xvi Abstract xviii 1 Introduction 1 1.1 The Data Deluge . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Mining the Web . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.1 Taxonomy of Web data . . . . . . . . . . . . . . . . . 8 1.3 Management of Data . . . . . . . . . . . . . . . . . . . . . . 10 1.3.1 Parallelism . . . . . . . . . . . . . . . . . . . . . . . . 11 1.3.2 Data Intensive Scalable Computing . . . . . . . . . 14 1.4 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2 Related Work 19 2.1 DISC systems . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.2 MapReduce . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.2.1 Computational Models and Extensions . . . . . . . 27 2.3 Streaming . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.3.1 S4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.4 Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 x
- 11. 3 SSJ 37 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.2 Problem definition and preliminaries . . . . . . . . . . . . . 40 3.3 Related work . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.3.1 MapReduce Term-Filtering (ELSA) . . . . . . . . . . 42 3.3.2 MapReduce Prefix-Filtering (VERN) . . . . . . . . . 44 3.4 SSJ Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.4.1 Double-Pass MapReduce Prefix-Filtering (SSJ-2) . . 46 3.4.2 Double-Pass MapReduce Prefix-Filtering with Re- mainder File (SSJ-2R) . . . . . . . . . . . . . . . . . 49 3.4.3 Partitioning . . . . . . . . . . . . . . . . . . . . . . . 52 3.5 Complexity analysis . . . . . . . . . . . . . . . . . . . . . . 53 3.6 Experimental evaluation . . . . . . . . . . . . . . . . . . . . 56 3.6.1 Running time . . . . . . . . . . . . . . . . . . . . . . 57 3.6.2 Map phase . . . . . . . . . . . . . . . . . . . . . . . . 59 3.6.3 Shuffle size . . . . . . . . . . . . . . . . . . . . . . . 62 3.6.4 Reduce phase . . . . . . . . . . . . . . . . . . . . . . 63 3.6.5 Partitioning the remainder file . . . . . . . . . . . . 65 3.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 4 SCM 67 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.2 Related work . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.3 Problem definition . . . . . . . . . . . . . . . . . . . . . . . 71 4.4 Application scenarios . . . . . . . . . . . . . . . . . . . . . . 72 4.5 Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.5.1 Computing the set of candidate edges . . . . . . . . 74 4.5.2 The STACKMR algorithm . . . . . . . . . . . . . . . 75 4.5.3 Adaptation in MapReduce . . . . . . . . . . . . . . 81 4.5.4 The GREEDYMR algorithm . . . . . . . . . . . . . . 84 4.5.5 Analysis of the GREEDYMR algorithm . . . . . . . . 85 4.6 Experimental evaluation . . . . . . . . . . . . . . . . . . . . 87 4.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 xi
- 12. 5 T.Rex 98 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.2 Related work . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 5.3 Problem definition and model . . . . . . . . . . . . . . . . . 106 5.3.1 Entity popularity . . . . . . . . . . . . . . . . . . . . 113 5.4 System overview . . . . . . . . . . . . . . . . . . . . . . . . 116 5.5 Learning algorithm . . . . . . . . . . . . . . . . . . . . . . . 119 5.5.1 Constraint selection . . . . . . . . . . . . . . . . . . 121 5.5.2 Additional features . . . . . . . . . . . . . . . . . . . 122 5.6 Experimental evaluation . . . . . . . . . . . . . . . . . . . . 123 5.6.1 Datasets . . . . . . . . . . . . . . . . . . . . . . . . . 123 5.6.2 Test set . . . . . . . . . . . . . . . . . . . . . . . . . . 125 5.6.3 Evaluation measures . . . . . . . . . . . . . . . . . . 126 5.6.4 Baselines . . . . . . . . . . . . . . . . . . . . . . . . . 128 5.6.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . 128 5.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 6 Conclusions 131 A List of Acronyms 135 References 137 xii
- 13. List of Figures 1.1 The petabyte age. . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Data Information Knowledge Wisdom hierarchy. . . . . . . 4 1.3 Complexity of contributed algorithms. . . . . . . . . . . . . 17 2.1 DISC architecture. . . . . . . . . . . . . . . . . . . . . . . . . 20 2.2 Data flow in the MapReduce programming paradigm. . . . 26 2.3 Overview of S4. . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.4 Twitter hashtag counting in S4. . . . . . . . . . . . . . . . . 33 3.1 ELSA example. . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.2 VERN example. . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.3 Pruned document pair: the left part (orange/light) has been pruned, the right part (blue/dark) has been indexed. 47 3.4 SSJ-2 example. . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.5 SSJ-2R example. . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.6 Running time. . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.7 Average mapper completion time. . . . . . . . . . . . . . . 59 3.8 Mapper completion time distribution. . . . . . . . . . . . . 60 3.9 Effect of Prefix-filtering on inverted list length distribution. 62 3.10 Shuffle size. . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.11 Average reducer completion time. . . . . . . . . . . . . . . 64 3.12 Remainder file and shuffle size varying K. . . . . . . . . . . 65 4.1 Example of a STACKMR run. . . . . . . . . . . . . . . . . . 80 xiii
- 14. 4.2 Communication pattern for iterative graph algorithms on MR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 4.3 Distribution of edge similarities for the datasets. . . . . . . 88 4.4 Distribution of capacities for the three datasets. . . . . . . . 89 4.5 flickr-small dataset: matching value and number of iterations as a function of the number of edges. . . . . . . . 92 4.6 flickr-large dataset: matching value and number of iterations as a function of the number of edges. . . . . . . . 93 4.7 yahoo-answers dataset: matching value and number of iterations as a function of the number of edges. . . . . . . . 94 4.8 Violation of capacities for STACKMR. . . . . . . . . . . . . . 95 4.9 Normalized value of the b-matching achieved by the GREEDY- MR algorithm as a function of the number of MapReduce iterations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 5.1 Osama Bin Laden trends on Twitter and news streams. . . . 101 5.2 Joplin tornado trends on Twitter and news streams. . . . . . 102 5.3 Cumulative Osama Bin Laden trends (news, Twitter and clicks). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 5.4 News-click delay distribution. . . . . . . . . . . . . . . . . . 114 5.5 Cumulative news-click delay distribution. . . . . . . . . . . 115 5.6 Overview of the T.REX system. . . . . . . . . . . . . . . . . 117 5.7 T.REX news ranking dataflow. . . . . . . . . . . . . . . . . . 119 5.8 Distribution of entities in Twitter. . . . . . . . . . . . . . . . 123 5.9 Distribution of entities in news. . . . . . . . . . . . . . . . . 124 5.10 Average discounted cumulated gain on related entities. . . 129 xiv
- 15. List of Tables 2.1 Major Data Intensive Scalable Computing (DISC) systems. 21 3.1 Symbols and quantities. . . . . . . . . . . . . . . . . . . . . 54 3.2 Complexity analysis. . . . . . . . . . . . . . . . . . . . . . . 54 3.3 Samples from the TREC WT10G collection. . . . . . . . . . 57 3.4 Statistics for the four algorithms on the three datasets. . . . 61 4.1 Dataset characteristics. |T|: number of items; |C|: number of users; |E|: total number of item-user pairs with non zero similarity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 5.1 Table of symbols. . . . . . . . . . . . . . . . . . . . . . . . . 107 5.2 MRR, precision and coverage. . . . . . . . . . . . . . . . . . 128 xv
- 16. Publications 1. G. De Francisci Morales, A. Gionis, C. Lucchese, “From Chatter to Head- lines: Harnessing the Real-Time Web for Personalized News Recommen- dations", WSDM’12, 5th ACM International Conference on Web Search and Data Mining, Seattle, 2012, pp. 153-162. 2. G. De Francisci Morales, A. Gionis, M. Sozio, “Social Content Matching in MapReduce”, PVLDB, Proceedings of the VLDB Endowment, 4(7):460-469, 2011. 3. R. Baraglia, G. De Francisci Morales, C. Lucchese, “Document Similarity Self-Join with MapReduce”, ICDM’10, 10th IEEE International Conference on Data Mining, Sydney, 2010, pp. 731-736. 4. G. De Francisci Morales, C. Lucchese, R. Baraglia, “Scaling Out All Pairs Similarity Search with MapReduce”, LSDS-IR’10, 8th Workshop on Large- Scale Distributed Systems for Information Retrieval, @SIGIR’10, Geneva, 2010, pp. 25-30. 5. G. De Francisci Morales, C. Lucchese, R. Baraglia, “Large-scale Data Anal- ysis on the Cloud”, XXIV Convegno Annuale del CMG-Italia, Roma, 2010. xvi
- 17. Presentations 1. G. De Francisci Morales, “Harnessing the Real-Time Web for Personalized News Recommendation”, Yahoo! Labs, Sunnyvale, 16 Februrary 2012. 2. G. De Francisci Morales, “Big Data and the Web: Algorithms for Data In- tensive Scalable Computing”, WSDM’12, Seattle, 8 Februrary 2012. 3. G. De Francisci Morales, “Social Content Matching in MapReduce”, Yahoo! Research, Barcelona, 10 March 2011. 4. G. De Francisci Morales, “Cloud Computing for Large Scale Data Analy- sis”, Yahoo! Research, Barcelona, 2 December 2010. 5. G. De Francisci Morales, “Scaling Out All Pairs Similarity Search with MapReduce”, Summer School on Social Networks, Lipari, 6 July 2010. 6. G. De Francisci Morales, “How to Survive the Data Deluge: Petabyte Scale Cloud Computing”, ISTI-CNR, Pisa, 18 January 2010. xvii
- 18. Abstract This thesis explores the problem of large scale Web mining by using Data Intensive Scalable Computing (DISC) systems. Web mining aims to extract useful information and models from data on the Web, the largest repository ever created. DISC systems are an emerging technology for processing huge datasets in parallel on large computer clusters. Challenges arise from both themes of research. The Web is heterogeneous: data lives in various formats that are best modeled in different ways. Effectively extracting information requires careful design of algorithms for specific categories of data. The Web is huge, but DISC systems offer a platform for building scalable solutions. However, they provide restricted computing primitives for the sake of performance. Efficiently harnessing the power of parallelism offered by DISC systems involves rethinking traditional algorithms. This thesis tackles three classical problems in Web mining. First we propose a novel solution to finding similar items in a bag of Web pages. Second we consider how to effectively distribute content from Web 2.0 to users via graph matching. Third we show how to harness the streams from the real-time Web to suggest news articles. Our main contribution lies in rethinking these problems in the context of massive scale Web mining, and in designing efficient MapReduce and streaming algorithms to solve these problems on DISC systems. xviii
- 19. Chapter 1 Introduction An incredible “data deluge” is currently drowning the world. Data sources are everywhere, from Web 2.0 and user-generated content to large scien- tific experiments, from social networks to wireless sensor networks. This massive amount of data is a valuable asset in our information society. Data analysis is the process of inspecting data in order to extract useful information. Decision makers commonly use this information to drive their choices. The quality of the information extracted by this pro- cess greatly benefits from the availability of extensive datasets. The Web is the biggest and fastest growing data repository in the world. Its size and diversity make it the ideal resource to mine for useful information. Data on the Web is very diverse in both content and format. Consequently, algorithms for Web mining need to take into account the specific characteristics of the data to be efficient. As we enter the “petabyte age”, traditional approaches for data analy- sis begin to show their limits. Commonly available data analysis tools are unable to keep up with the increase in size, diversity and rate of change of the Web. Data Intensive Scalable Computing is an emerging alterna- tive technology for large scale data analysis. DISC systems combine both storage and computing in a distributed and virtualized manner. These systems are built to scale to thousands of computers, and focus on fault tolerance, cost effectiveness and ease of use. 1
- 20. 1.1 The Data Deluge How would you sort 1GB of data? Today’s computers have enough memory to keep this quantity of data, so any optimal in-memory al- gorithm will suffice. What if you had to sort 100 GB of data? Even if systems with more than 100 GB of memory exist, they are by no means common or cheap. So the best solution is to use a disk based sorting al- gorithm. However, what if you had 10 TB of data to sort? At a transfer rate of about 100 MB/s for a normal disk it would take more than one day to make a single pass over the dataset. In this case the bandwidth between memory and disk is the bottleneck. In any case, today’s disks are usually 1 to 2 TB in size, which means that just to hold the data we need multiple disks. In order to obtain acceptable completion times, we also need to use multiple computers and a parallel algorithm. This example illustrates a general point: the same problem at differ- ent scales needs radically different solutions. In many cases we even need change the model we use to reason about the problem because the simplifying assumptions made by the models do not hold at every scale. Citing Box and Draper (1986) “Essentially, all models are wrong, but some are useful”, and arguably “most of them do not scale”. Currently, an incredible “data deluge” is drowning the world. The amount of data we need to sift through every day is enormous. For in- stance the results of a search engine query are so many that we are not able to examine all of them, and indeed the competition now focuses the top ten results. This is just an example of a more general trend. The issues raised by large datasets in the context of analytical ap- plications are becoming ever more important as we enter the so-called “petabyte age”. Figure 1.1 shows the sizes of the datasets for problems we currently face (Anderson, 2008). The datasets are orders of magni- tude greater than what fits on a single hard drive, and their management poses a serious challenge. Web companies are currently facing this issue, and striving to find efficient solutions. The ability to manage and ana- lyze more data is a distinct competitive advantage for them. This issue has been labeled in various ways: petabyte scale, Web scale or “big data”. 2
- 21. Figure 1.1: The petabyte age. But how do we define “big data”? The definition is of course relative and evolves in time as technology progresses. Indeed, thirty years ago one terabyte would be considered enormous, while today we are com- monly dealing with such quantity of data. Gartner (2011) puts the focus not only on size but on three different dimensions of growth for data, the 3V: Volume, Variety and Velocity. The data is surely growing in size, but also in complexity as it shows up in different formats and from different sources that are hard to integrate, and in dynamicity as it arrives continuously, changes rapidly and needs to be processed as fast as possible. Loukides (2010) offers a different point of view by saying that big data is “when the size of the data itself becomes part of the problem” and “traditional techniques for working with data run out of steam”. Along the same lines, Jacobs (2009) states that big data is “data whose size forces us to look beyond the tried-and-true methods that are preva- lent at that time”. This means that we can call big an amount of data that forces us to use or create innovative methodologies. We can think that the intrinsic characteristics of the object to be an- alyzed demand modifications to traditional data managing procedures. 3
- 22. Understanding Connectedness Data Knowledge Wisdom Information Understand Relations Understand Patterns Understand Principles Figure 1.2: Data Information Knowledge Wisdom hierarchy. Alternatively, we can take the point of view of the subject who needs to manage the data. The emphasis is thus on user requirements such as throughput and latency. In either case, all the previous definitions hint to the fact that big data is a driver for research. But why are we interested in data? It is common belief that data with- out a model is just noise. Models are used to describe salient features in the data, which can be extracted via data mining. Figure 1.2 depicts the popular Data Information Knowledge Wisdom (DIKW) hierarchy (Row- ley, 2007). In this hierarchy data stands at the lowest level and bears the smallest level of understanding. Data needs to be processed and con- densed into more connected forms in order to be useful for event com- prehension and decision making. Information, knowledge and wisdom are these forms of understanding. Relations and patterns that allow to gain deeper awareness of the process that generated the data, and prin- ciples that can guide future decisions. 4
- 23. For data mining, the scaling up of datasets is a “double edged” sword. On the one hand, it is an opportunity because “no data is like more data”. Deeper insights are possible when more data is available (Halevy et al., 2009). Oh the other hand, it is a challenge. Current methodologies are often not suitable to handle huge datasets, so new solutions are needed. The large availability of data potentially enables more powerful anal- ysis and unexpected outcomes. For example, Google Flu Trends can detect regional flu outbreaks up to ten days faster than the Center for Disease Control and Prevention by analyzing the volume of flu-related queries to the Web search engine (Ginsberg et al., 2008). Companies like IBM and Google are using large scale data to solve extremely challeng- ing problems like avoiding traffic congestion, designing self-driving cars or understanding Jeopardy riddles (Loukides, 2011). Chapter 2 presents more examples of interesting large scale data analysis problems. Data originates from a wide variety sources. Radio-Frequency Iden- tification (RFID) tags and Global Positioning System (GPS) receivers are already spread all around us. Sensors like these produce petabytes of data just as a result of their sheer numbers, thus starting the so called “industrial revolution of data” (Hellerstein, 2008). Scientific experiments are also a huge data source. The Large Hadron Collider at CERN is expected to generate around 50 TB of raw data per day. The Hubble telescope captured millions of astronomical images, each weighting hundreds of megabytes. Computational biology experi- ments like high-throughput genome sequencing produce large quantities of data that require extensive post-processing. The focus of our work is directed to another massive source of data: the Web. The importance of the Web from the scientific, economical and political point of view has grown dramatically over the last ten years, so much that internet access has been declared a human right by the United Nations (La Rue, 2011). Web users produce vast amounts of text, audio and video contents in the Web 2.0. Relationships and tags in social net- works create massive graphs spanning millions of vertexes and billions of edges. In the next section we highlight some of the opportunities and challenges found when mining the Web. 5
- 24. 1.2 Mining the Web The Web is easily the single largest publicly accessible data source in the world (Liu, 2007). The continuous usage of the Web has accelerated its growth. People and companies keep adding to the already enormous mass of pages already present. In the last decade the Web has increased its importance to the point of becoming the center of our digital lives (Hammersley, 2011). People shop and read news on the Web, governments offer public services through it and enterprises develop Web marketing strategies. Investments in Web advertising have surpassed the ones in television and newspaper in most countries. This is a clear testament to the importance of the Web. The estimated size of the indexable Web was at least 11.5 billion pages as of January 2005 (Gulli and Signorini, 2005). Today, the Web size is estimated between 50 and 100 billion pages and roughly doubling every eight months (Baeza-Yates and Ribeiro-Neto, 2011), faster than Moore’s law. Furthermore, the Web has become infinite for practical purpose, as it is possible to generate an infinite number of dynamic pages. As a result, there is on the Web an abundance of data with growing value. The value of this data lies in being representative of collective user behavior. It is our digital footprint. By analyzing a large amount of these traces it is possible to find common patterns, extract user models, make better predictions, build smarter products and gain a better understand- ing of the dynamics of human behavior. Enterprises have started to re- alize on which gold mine they are sitting on. Companies like Facebook and Twitter base their business model entirely on collecting user data. Data on the Web is often produced as a byproduct of online activity of the users, and is sometimes referred to as data exhaust. This data is silently collected while the users are pursuing their own goal online, e.g. query logs from search engines, co-buying and co-visiting statistics from online shops, click through rates from news and advertisings, and so on. This process of collecting data automatically can scale much further than traditional methods like polls and surveys. For example it is possi- ble to monitor public interest and public opinion by analyzing collective 6
- 25. click behavior in news portals, references and sentiments in blogs and micro-blogs or query terms in search engines. As another example, Yahoo! and Facebook (2011) are currently repli- cating the famous “small world” experiment ideated by Milgram. They are leveraging the social network created by Facebook users to test the “six degrees of separation” hypothesis on a planetary scale. The large number of users allows to address the critiques of selection and non- response bias made to the original experiment. Let us now more precisely define Web mining. Web mining is the ap- plication of data mining techniques to discover patterns from the Web. According to the target of the analysis at hand, Web mining can be cat- egoryzed into three different types: Web structure mining, Web content mining and Web usage mining (Liu, 2007). Web structure mining mines the hyperlink structure of the Web using graph theory. For example, links are used by search engines to find important Web pages, or in social networks to discover communi- ties of users who share common interests. Web content mining analyzes Web page contents. Web content mining differs from traditional data and text mining mainly because of the semi-structured and multimedial nature of Web pages. For exam- ple, it is possible to automatically classify and cluster Web pages according to their topics but it is also possible to mine customer product reviews to discover consumer sentiments. Web usage mining extracts information from user access patterns found in Web server logs, which record the pages visited by each user, and from search patterns found in query logs, which record the terms searched by each user. Web usage mining investigates what users are interested in on the Web. Mining the Web is typically deemed highly promising and rewarding. However, it is by no means an easy task and there is a flip side of the coin: data found on the Web is extremely noisy. 7
- 26. The noise comes from two main sources. First, Web pages are com- plex and contain many pieces of information, e.g., the main content of the page, links, advertisements, images and scripts. For a particular ap- plication, only part of the information is useful and the rest is consid- ered noise. Second, the Web is open to anyone and does not enforce any quality control of information. Consequently a large amount of informa- tion on the Web is of low quality, erroneous, or even misleading, e.g., automatically generated spam, content farms and dangling links. This applies also to Web server logs and Web search engine logs, where er- ratic behaviors, automatic crawling, spelling mistakes, spam queries and attacks introduce a large amount of noise. The signal, i.e. the useful part of the information, is often buried un- der a pile of dirty, noisy and unrelated data. It is the duty of a data ana- lyst to “separate the wheat from the chaff” by using sophisticated cleaning, pre-processing and mining techniques. This challenge is further complicated by the sheer size of the data. Datasets coming from the Web are too large to handle using traditional systems. Storing, moving and managing them are complex tasks by themselves. For this reason a data analyst needs the help of powerful yet easy to use systems that abstract away the complex machinery needed to deliver the required performance. The goal of these systems is to re- duce the time-to-insight by speeding up the design-prototype-test cycle in order to test a larger number of hypothesis, as detailed in Section 1.3. 1.2.1 Taxonomy of Web data The Web is a very diverse place. It is an open platform where anybody can add his own contribution. Resultingly, information on the Web is heterogeneous. Almost any kind of information can be found on it, usu- ally reproduced in a proliferation of different formats. As a consequence, the categories of data available on the Web are quite varied. Data of all kinds exist on the Web: semi-structured Web pages, struc- tured tables, unstructured texts, explicit and implicit links, and multime- dia files (images, audios, and videos) just to name a few. A complete 8
- 27. classification of the categories of data on the Web is out of the scope of this thesis. However, we present next what we consider to be the most common and representative categories, the ones on which we focus our attention. Most of the Web fits one of these three categories: Bags are unordered collections of items. The Web can be seen as a col- lections of documents when ignoring hyperlinks. Web sites that collect one specific kind of items (e.g. flickr or YouTube) can also be modeled as bags. The items in the bag are typically represented as sets, multisets or vectors. Most classical problems like similarity, clustering and frequent itemset mining are defined over bags. Graphs are defined by a set of vertexes connected by a set of edges. The Web link structure and social networks fit in this category. Graph are an extremely flexible data model as almost anything can be seen as a graph. They can also be generated from predicates on a set of items (e.g. similarity graph, query flow graph). Graph algorithms like PageRank, community detection and matching are commonly employed to solve problems in Web and social network mining. Streams are unbounded sequences of items ordered by time. Search queries and click streams are traditional examples, but streams are generated as well by news portals, micro-blogging services and real-time Web sites like twitter and “status updates” on social net- works like Facebook, Google+ and LinkedIn. Differently from time series, Web streams are textual, multimedial or have rich metadata. Traditional stream mining problems are clustering, classification and estimation of frequency moments. Each of these categories has its own characteristics and complexities. Bags of items include very large collections whose items can be analyzed independently in parallel. However this lack of structure can also com- plicate analysis as in the case of clustering and nearest neighbor search, where each item can be related to any other item in the bag. In contrast, graphs have a well defined structure that limits the lo- cal relationships that need to be taken into account. For this reason lo- cal properties like degree distribution and clustering coefficient are very 9
- 28. easy to compute. However global properties such as diameter and girth generally require more complex iterative algorithms. Finally, streams get continuously produced and a large part of their value is in their freshness. As such, they cannot be analyzed in batches and need to be processed as fast as possible in an online fashion. For the reasons just described, the algorithms and the methodologies needed to analyze each category of data are quite different from each other. As detailed in Section 1.4, in this work we present three different algorithms for large scale data analysis, each one explicitly tailored for one of these categories of data. 1.3 Management of Data Providing data for analysis is a problem that has been extensively stud- ied. Many solutions exist but the traditional approach is to employ a Database Management System (DBMS) to store and manage the data. Modern DBMS originate in the ’70s, when Codd (1970) introduced the famous relational model that is still in use today. The model intro- duces the familiar concepts of tabular data, relation, normalization, pri- mary key, relational algebra and so on. The original purpose of DBMSs was to process transactions in busi- ness oriented processes, also known as Online Transaction Processing (OLTP). Queries were written in Structured Query Language (SQL) and run against data modeled in relational style. On the other hand, cur- rently DBMSs are used in a wide range of different areas: besides OLTP, we have Online Analysis Processing (OLAP) applications like data ware- housing and business intelligence, stream processing with continuous queries, text databases and much more (Stonebraker and Çetintemel, 2005). Furthermore, stored procedures are preferred over plain SQL for performance reasons. Given the shift and diversification of application fields, it is not a surprise that most existing DBMSs fail to meet today’s high performance requirements (Stonebraker et al., 2007a,b). High performance has always been a key issue in database research. There are usually two approaches to achieve it: vertical and horizon- 10
- 29. tal. The former is the simplest, and consists in adding resources (cores, memory, disks) to an existing system. If the resulting system is capable of taking advantage of the new resources it is said to scale up. The inherent limitation of this approach is that the single most powerful system avail- able on earth could not suffice. The latter approach is more complex, and consists in adding new separate systems in parallel. The multiple systems are treated as a single logical unit. If the system achieves higher performance it is said to scale out. However, the result is a parallel sys- tem with all the hard problems of concurrency. 1.3.1 Parallelism Typical parallel systems are divided into three categories according to their architecture: shared memory, shared disk or shared nothing. In the first category we find Symmetric Multi-Processors (SMPs) and large parallel machines. In the second one we find rack based solutions like Storage Area Network (SAN) or Network Attached Storage (NAS). The last category includes large commodity clusters interconnected by a local network and is deemed to be the most scalable (Stonebraker, 1986). Parallel Database Management Systems (PDBMSs) (DeWitt and Gray, 1992) are the result of these considerations. They attempt to achieve high performance by leveraging parallelism. Almost all the designs of PDBMSs use the same basic dataflow pattern for query processing and horizontal partitioning of the tables on a cluster of shared nothing ma- chines for data distribution (DeWitt et al., 1990). Unfortunately, PDBMSs are very complex systems. They need fine tuning of many “knobs” and feature simplistic fault tolerance policies. In the end, they do not provide the user with adequate ease of installation and administration (the so called “one button” experience), and flexibility of use, e.g., poor support of User Defined Functions (UDFs). To date, despite numerous claims about their scalability, PDBMSs have proven to be profitable only up to the tens or hundreds of nodes. It is legitimate to question whether this is the result of a fundamental theoretical problem in the parallel approach. 11
- 30. Parallelism has some well known limitations. Amdahl (1967) argued in favor of a single-processor approach to achieve high performance. In- deed, the famous “Amdahl’s law” states that the parallel speedup of a program is inherently limited by the inverse of his serial fraction, the non parallelizable part of the program. His law also defines the concept of strong scalability, in which the total problem size is fixed. Equation 1.1 specifies Amdahl’s law for N parallel processing units where rs and rp are the serial and parallel fraction of the program (rs + rp = 1) SpeedUp(N) = 1 rs + rp N (1.1) Nevertheless, parallelism has a theoretical justification. Gustafson (1988) re-evaluated Amdahl’s law using a different assumption, i.e. that the problem sizes increases with the computing units. In this case the problem size per unit is fixed. Under this assumption, the achievable speedup is almost linear, as expressed by Equation 1.2. In this case rs and rp are the serial and parallel fraction measured on the parallel sys- tem instead of the serial one. Equation 1.2 defines the concept of scaled speedup or weak scalability SpeedUp(N) = rs + rp ∗ N = N + (1 − N) ∗ rs (1.2) Even though the two equations are mathematically equivalent (Shi, 1996), they make drastically different assumptions. In our case the size of the problem is large and ever growing. Hence it seems appropriate to adopt Gustafson’s point of view, which justifies the parallel approach. Parallel computing has a long history. It has traditionally focused on “number crunching”. Common applications were tightly coupled and CPU intensive (e.g. large simulations or finite element analysis). Control- parallel programming interfaces like Message Passing Interface (MPI) or Parallel Virtual Machine (PVM) are still the de-facto standard in this area. These systems are notoriously hard to program. Fault tolerance is diffi- cult to achieve and scalability is an art. They require explicit control of parallelism and are called “the assembly language of parallel computing”. 12
- 31. In stark contrast with this legacy, a new class of parallel systems has emerged: cloud computing. Cloud systems focus on being scalable, fault tolerant, cost effective and easy to use. Lately cloud computing has received a substantial amount of atten- tion from industry, academia and press. As a result, the term “cloud computing” has become a buzzword, overloaded with meanings. There is lack of consensus on what is and what is not cloud. Even simple client- server applications are sometimes included in the category (Creeger, 2009). The boundaries between similar technologies are fuzzy, so there is no clear distinction among grid, utility, cloud, and other kinds of comput- ing technologies. In spite of the many attempts to describe cloud com- puting (Mell and Grance, 2009), there is no widely accepted definition. However, within cloud computing, there is a more cohesive subset of technologies which is geared towards data analysis. We refer to this subset as Data Intensive Scalable Computing (DISC) systems. These sys- tems are aimed mainly at I/O intensive tasks, are optimized for dealing with large amounts of data and use a data-parallel approach. An inter- esting feature is they are “dispersed”: computing and storage facilities are distributed, abstracted and intermixed. These systems attempt to move computation as close to data as possible because moving large quanti- ties of data is expensive. Finally, the burden of dealing with the issues caused by parallelism is removed from the programmer. This provides the programmer with a scale-agnostic programming model. The data-parallel nature of DISC systems abstracts away many of the details of parallelism. This allows to design clean and elegant algorithms. DISC systems offer a limited interface that allows to make strong as- sumptions about user code. This abstraction is useful for performance optimization, but constrains the class of algorithms that can be run on these systems. In this sense, DISC systems are not general purpose com- puting systems, but are specialized in solving a specific class of problems. DISC systems are a natural alternative to PDBMSs when dealing with large scale data. As such, a fierce debate is currently taking place, both in industry and academy, on which is the best tool (Dean and S. Ghemawat, 2010; DeWitt and Stonebraker, 2008; Stonebraker et al., 2010). 13
- 32. 1.3.2 Data Intensive Scalable Computing Let us highlight some of the requirements for a system used to perform data intensive computing on large datasets. Given the effort to find a novel solution and the fact that data sizes are ever growing, this solution should be applicable for a long period of time. Thus the most important requirement a solution has to satisfy is scalability. Scalability is defined as “the ability of a system to accept increased input volume without impacting the profits”. This means that the gains from the input increment should be proportional to the increment itself. This is a broad definition used also in other fields like economy. For a system to be fully scalable, the size of its input should not be a design parameter. Forcing the system designer to take into account all possible deployment sizes in order to cope with different input sizes leads to a scalable architecture without fundamental bottlenecks. However, apart from scalability, there are other requirements for a large scale data intensive computing system. Real world systems cost money to build and operate. Companies attempt to find the most cost effective way of building a large system because it usually requires a sig- nificant money investment. Partial upgradability is an important money saving feature, and is more easily attained with a loosely coupled sys- tem. Operational costs like system administrators’ salaries account for a large share of the budget of IT departments. To be profitable, large scale systems must require as little human intervention as possible. Therefore autonomic systems are preferable, systems that are self-configuring, self- tuning and self-healing. In this respect fault tolerance is a key property. Fault tolerance is “the property of a system to operate properly in spite of the failure of some of its components”. When dealing with a large number of systems, the probability that a disk breaks or a server crashes raises dramatically: it is the norm rather than the exception. A performance degradation is acceptable as long as the systems does not halt completely. A denial of service of a system has a negative economic impact, especially for Web-based companies. The goal of fault tolerance techniques is to create a highly available system. 14
- 33. To summarize, a large scale data analysis system should be scalable, cost effective and fault tolerant. To make our discussion more concrete we give some examples of DISC systems. A more detailed overview can be found in Chapter 2 while here we just quickly introduce the systems we use in our research. While other similar systems exist, we have chosen these systems be- cause of their availability as open source software and because of their widespread adoption both in academia and in industry. These factors increase the reusability of the results of our research and the chances of having practical impact on real-world problems. The systems we make use of in this work implement two different paradigms for processing massive datasets: MapReduce (MR) and stream- ing. MapReduce offers the capability to analyze massive amounts of stored data while streaming solutions are designed to process a mul- titude of updates every second. We provide a detailed descriptions of these paradigms in Chapter 2. Hadoop1 is a distributed computing framework that implements the MapReduce paradigm(Dean and Ghemawat, 2004) together with a com- panion distributed file system called Hadoop Distributed File System (HDFS). Hadoop enables the distributed processing of huge datasets across clusters of commodity computers by means of a simple functional programming model. A mention goes to Pig2 , a high level framework for data manipulation that runs on top of Hadoop (Olston et al., 2008). Pig is a very useful tool for data exploration, pre-processing and cleaning. Finally, S43 is a distributed scalable stream processing engine (Neumeyer et al., 2010). While still a young project, its potential lies in complement- ing Hadoop for stream processing. 1http://hadoop.apache.org 2http://pig.apache.org 3http://incubator.apache.org/s4 15
- 34. 1.4 Contributions DISC systems are an emerging technology in the data analysis field that can be used to capitalize on massive datasets coming from the Web. “There is no data like more data” is a famous motto that epitomizes the opportunity to extract significant information by exploiting very large volumes of data. Information represents a competitive advantage for actors operating in the information society, an advantage that is all the greater the sooner it is achieved. Therefore, in the limit online analytics will become an invaluable support for decision making. To date, DISC systems have been successfully employed for batch processing, while their use for online analytics has not received much attention and is still an open area of research. Many data analysis algo- rithms spanning different application areas have been already proposed for DISC systems. So far, speedup and scalability results are encourag- ing. We give an overview of these algorithms in Chapter 2. However, it is not clear in the research community which problems are a good match for DISC systems. More importantly, the ingredients and recipes for building a successful algorithm are still hidden. Design- ing efficient algorithms for these systems requires thinking at scale, care- fully taking into account the characteristics of input data, trading off communication and computing and addressing skew and load balanc- ing problems. Meeting these requirements on a system with restricted primitives is a challenging task and an area for research. This thesis explores the landscape of algorithms for Web mining on DISC systems and provides theoretical and practical insights on algo- rithm design and performance optimization. Our work builds on previous research in Data Mining, Information Retrieval and Machine Learning. The methodologies developed in these fields are essential to make sense of data on the Web. We also leverage Distributed Systems and Database research. The systems and techniques studied in these fields are the key to get an acceptable performance on Web-scale datasets. 16
- 35. Algorithm Structure DataComplexity MR-IterativeMR-Optimized S4-Streaming & MR Bags Streams & Graphs Graphs Social Content Matching Similarity Self-Join Personalized Online News Recommendation Figure 1.3: Complexity of contributed algorithms. Concretely, our contributions can be mapped as shown in Figure 1.3. We tackle three different problems that involve Web mining tasks on dif- ferent categories of data. For each problem, we provide algorithms for Data Intensive Scalable Computing systems. First, we tackle the problem of similarity on bags of Web documents in Chapter 3. We present SSJ-2 and SSJ-2R, two algorithms specifically designed for the MapReduce programming paradigm. These algorithms are batch oriented and operate in a fixed number of steps. Second, we explore graph matching in Chapter 4. We propose an ap- plication of matching to distribution of content from social media and Web 2.0. We describe STACKMR and GREEDYMR, two iterative MapRe- duce algorithms with different performance and quality properties. Both algorithms provide approximation guarantees and scale to huge datasets. 17
- 36. Third, we investigate news recommendation for social network users in Chapter 5. We propose a solution that takes advantage of the real- time Web to provide personalized and timely suggestions. We present T.REX, a methodology that combines stream and graph processing and is amenable to parallelization on stream processing engines like S4. To summarize, the main contribution of this thesis lies in addressing classical problems like similarity, matching and recommendation in the context of Web mining and in providing efficient and scalable solutions that harness the power of DISC systems. While pursuing this general objective we use some more specific goals as concrete stepping stones. In Chapter 3 we show that carefully designing algorithms specifically for MapReduce gives substantial performance advantages over trivial parallelization. By leveraging efficient communication patterns SSJ-2R outperforms state-of-the-art algorithms for similarity join in MapReduce by almost five times. Designing efficient MapReduce algorithms requires rethinking classical algorithms rather than using them as black boxes. By applying this principle we provide scalable algorithms for exact similar- ity computation without any need to tradeoff precision for performance. In Chapter 4 we propose the first solution to the graph matching problem in MapReduce. STACKMR and GREEDYMR are two algorithms for graph matching with provable approximation guarantees and high practical value for large real-world systems. We further propose a gen- eral scalable computational pattern for iterative graph mining in MR. This pattern can support a variety of algorithms and we show how to apply it to the two aforementioned algorithms for graph matching. Finally in Chapter 5 we describe a novel methodology that combines several signals from the real-time Web to predict user interest. T.REX is able to harnesses information extracted from user-generated content, so- cial circles and topic popularity to provide personalized and timely news suggestions. The proposed system combines offline iterative computa- tion on MapReduce and online processing of incoming data in a stream- ing fashion. This feature allows both to provide always fresh recommen- dations and to cope with the large amount of input data. 18
- 37. Chapter 2 Related Work In this chapter we give an overview of related work in terms of systems, paradigms and algorithms for large scale Web mining. We start by describing a general framework for DISC systems. Large scale data challenges have spurred the design of a multitude of new DISC systems. Here we review the most important ones and classify them ac- cording to our framework in a layered architecture. We further distin- guish between batch and online systems to underline their different tar- gets in the data and application spectrum. These tools compose the big data software stack used to tackle data intensive computing problems. Then we offer a more detailed overview of the two most important paradigms for large scale Web mining: MapReduce and streaming. These two paradigms are able to cope with huge or even unbounded datasets. While MapReduce offers the capability to analyze massive amounts of stored data, streaming solutions offer the ability to process a multitude of updates per second with low latency. Finally, we review some of the most influential algorithms for large scale Web mining on DISC systems. We focus mainly on MapReduce algorithms, which have received the largest share of attention. We show different kind of algorithms that have been proposed in the literature to process different types of data on the Web. 19
- 38. 2.1 DISC systems Even though existing DISC systems are very diverse, they share many common traits. For this reason we propose a general architecture of DISC systems, that captures the commonalities in the form of a multi-layered stack, as depicted in Figure 2.1. A complete DISC solution is usually devised by assembling multiple components. We classify the various components in three layers and two sublayers. Coordination Computation High Level Languages Distributed Data Data Abstraction Figure 2.1: DISC architecture. At the lowest level we find a coordination layer that serves as a basic building block for the distributed services higher in the stack. This layer deals with basic concurrency issues. The distributed data layer builds on top of the coordination one. This layer deals with distributed data access, but unlike a traditional dis- 20
- 39. tributed file system it does not offer standard POSIX semantics for the sake of performance. The data abstraction layer is still part of the data layer and offers different, more sophisticated interfaces to data. The computation layer is responsible for managing distributed pro- cessing. As with the data layer, generality is sacrificed for performance. Only embarrassingly data parallel problems are commonly solvable in this framework. The high level languages layer encompasses a number of languages, interfaces and systems that have been developed to sim- plify and enrich access to the computation layer. Table 2.1: Major DISC systems. Batch Online High Level Languages Sawzall, SCOPE, Pig Latin, Hive, DryadLINQ, FlumeJava, Cascading, Crunch Computation MapReduce, Hadoop, Dryad, Pregel, Giraph, Hama S4, Storm, Akka Data Abstraction BigTable, HBase, PNUTS, Cassandra, Voldemort Distributed Data GFS, HDFS, Cosmos Dynamo Coordination Chubby, Zookeeper Table 2.1 classifies some of the most popular DISC systems. In the coordination layer we find two implementations of a consensus algorithm. Chubby (Burrows, 2006) is an implementation of Paxos (Lam- port, 1998) while Zookeeper (Hunt et al., 2010) implements ZAB (Reed and Junqueira, 2008). They are distributed services for maintaining con- figuration information, naming, providing distributed synchronization and group services. The main characteristics of these services are very high availability and reliability, thus sacrificing high performance. 21
- 40. On the next level, the distributed data layer presents different kinds of data storages. A common feature in this layer is to avoid full POSIX semantic in favor of simpler ones. Furthermore, consistency is somewhat relaxed for the sake of performance. HDFS 1 , Google File System (GFS) (Ghemawat et al., 2003) and Cos- mos (Chaiken et al., 2008) are distributed file systems geared towards large batch processing. They are not general purpose file systems. For example, in HDFS files can only be appended but not modified and in GFS a record might get appended more than once (at least once seman- tics). They use large blocks of 64 MB or more, which are replicated for fault tolerance. Dynamo (DeCandia et al., 2007) is a low latency key- values store used at Amazon. It has a Peer-to-Peer (P2P) architecture that uses consistent hashing for load balancing and a gossiping protocol to guarantee eventual consistency (Vogels, 2008). The systems described above are either mainly append-only and batch oriented file systems or simple key-value stores. However, it is sometime convenient to access data in a different way, e.g. by using richer data models or by employing read/write operations. Data abstractions built on top of the aforementioned systems serve these purposes. BigTable (Chang et al., 2006) and HBase2 are non-relational data stores. They are actually multidimensional, sparse, sorted maps designed for semi-structured or non structured data. They provide random, realtime read/write access to large amounts of data. Access to data is provided via primary key only, but each key can have more than one column. PNUTS (Cooper et al., 2008) is a similar storage service developed by Yahoo! that leverages geographic distribution and caching, but offers limited consistency guarantees. Cassandra (Lakshman and Malik, 2010) is an open source Apache project initially developed by Facebook. It fea- tures a BigTable-like interface on a Dynamo-style infrastructure. Volde- mort3 is an open source non-relational database built by LinkedIn, basi- cally a large persistent Distributed Hash Table (DHT). 1http://hadoop.apache.org/hdfs 2http://hbase.apache.org 3http://project-voldemort.com 22
- 41. In the computation layer we find paradigms for large scale data in- tensive computing. They are mainly dataflow paradigms with support for automated parallelization. We can recognize the same pattern found in previous layers also here: trade off generality for performance. MapReduce (Dean and Ghemawat, 2004) is a distributed computing engine developed by Google, while Hadoop4 is an open source clone. A more detailed description of this framework is presented in Section 2.2. Dryad (Isard et al., 2007) is Microsoft’s alternative to MapReduce. Dryad is a distributed execution engine inspired by macro-dataflow techniques. Programs are specified by a Direct Acyclic Graph (DAG) whose ver- texes are operations and whose edges are data channels. The system takes care of scheduling, distribution, communication and execution on a cluster. Pregel (Malewicz et al., 2010), Giraph5 and Hama (Seo et al., 2010) are systems that implement the Bulk Synchronous Parallel (BSP) model (Valiant, 1990). Pregel is a large scale graph processing system developed by Google. Giraph implements Pregel’s interface as a graph processing library that runs on top of Hadoop. Hama is a generic BSP framework for matrix processing. S4 (Neumeyer et al., 2010) by Yahoo!, Storm6 by Twitter and Akka7 are distributed stream processing engines that implement the Actor model (Agha, 1986) They target a different part of the spectrum of big data, namely online processing of high-speed and high-volume event streams. Inspired by MapReduce, they provide a way to scale out stream process- ing on a cluster by using simple functional components. At the last level we find high level interfaces to these computing sys- tems. These interfaces are meant to simplify writing programs for DISC systems. Even though this task is easier than writing custom MPI code, DISC systems still offer fairly low level programming interfaces, which require the knowledge of a full programming language. The interfaces at this level allow even non programmers to perform large scale processing. Sawzall (Pike et al., 2005), SCOPE (Chaiken et al., 2008) and Pig Latin 4http://hadoop.apache.org 5http://incubator.apache.org/giraph 6https://github.com/nathanmarz/storm 7http://akka.io 23
- 42. (Olston et al., 2008) are special purpose scripting languages for MapRe- duce, Dryad and Hadoop. They are able to perform filtering, aggrega- tion, transformation and joining. They share many features with SQL but are easy to extend with UDFs. These tools are invaluable for data explo- ration and pre-processing. Hive (Thusoo et al., 2009) is a data warehous- ing system that runs on top of Hadoop and HDFS. It answers queries expressed in a SQL-like language called HiveQL on data organized in tabular format. Flumejava (Chambers et al., 2010), DryadLINQ (Yu et al., 2008), Cascading8 and Crunch9 are native language integration libraries for MapReduce, Dryad and Hadoop. They provide an interface to build pipelines of operators from traditional programming languages, run them on a DISC system and access results programmatically. 2.2 MapReduce When dealing with large datasets like the ones coming from the Web, the costs of serial solutions are not acceptable. Furthermore, the size of the dataset and supporting structures (indexes, partial results, etc...) can easily outgrow the storage capabilities of a single node. The MapReduce paradigm (Dean and Ghemawat, 2004, 2008) is designed to deal with the huge amount of data that is readily available nowadays. MapReduce has gained increasing attention due to its adaptability to large clusters of computers and to the ease of developing highly parallel and fault- tolerant solutions. MR is expected to become the normal way to deal with massive datasets in the future (Rajaraman and Ullman, 2010). MapReduce is a distributed computing paradigm inspired by con- cepts from functional languages. More specifically, it is based on two higher order functions: Map and Reduce. The Map function reads the input as a list of key-value pairs and applies a UDF to each pair. The result is a second list of intermediate key-value pairs. This list is sorted and grouped by key in the shuffle phase, and used as input to the Reduce function. The Reduce function applies a second UDF to each intermedi- 8http://www.cascading.org 9https://github.com/cloudera/crunch 24
- 43. ate key with all its associated values to produce the final result. The two phases are strictly non overlapping. The general signatures of the two phases of a MapReduce computation are as follows: Map: k1, v1 → [ k2, v2 ] Reduce: k2, [v2] → [ k3, v3 ] The Map and Reduce function are purely functional and thus without side effects. This property makes them easily parallelizable because each input key-value is independent from the other ones. Fault tolerance is also easily achieved by just re-executing the failed function instance. MapReduce assumes a distributed file systems from which the Map instances retrieve their input data. The framework takes care of mov- ing, grouping and sorting the intermediate data produced by the various mappers (tasks that execute the Map function) to the corresponding re- ducers (tasks that execute the Reduce function) . The programming interface is easy to use and does not require any explicit control of parallelism. A MapReduce program is completely de- fined by the two UDFs run by mappers and reducers. Even though the paradigm is not general purpose, many interesting algorithms can be implemented on it. The most paradigmatic application is building an in- verted index for a Web search engine. Simplistically, the algorithm reads the crawled and filtered web documents from the file system, and for every word it emits the pair word, doc_id in the Map phase. The Re- duce phase simply groups all the document identifiers associated with the same word word, [doc_id1, doc_id2, . . .] to create an inverted list. The MapReduce data flow is illustrated in Figure 2.2. The mappers read their data from the distributed file system. The file system is nor- mally co-located with the computing system so that most reads are local. Each mapper reads a split of the input, applies the Map function to the key-value pair and potentially produces one or more output pairs. Map- pers sort and write intermediate values on the local disk. Each reducer in turn pulls the data from various remote locations. Intermediate key-value pairs are already partitioned and sorted by key by the mappers, so the reducer just merge-sorts the different partitions to 25
- 44. DFS Input 1 Input 2 Input 3 MAP MAP MAP REDUCE REDUCE DFS Output 1 Output 2 Shuffle Merge & GroupPartition & Sort Figure 2.2: Data flow in the MapReduce programming paradigm. group the same keys together. This phase is called shuffle and is the most expensive in terms of I/O operations. The shuffle phase can partially overlap with the Map phase. Indeed, intermediate results from mappers can start being transferred as soon as they are written to disk. In the last phase each reducer applies the Reduce function to the intermediate key-value pairs and write the final output to the file system. MapReduce has become the de-fact standard for the development of large scale applications running on thousand of inexpensive machines, especially with the release of its open source implementation Hadoop. Hadoop is an open source MapReduce implementation written in Java. Hadoop also provides a distributed file system called HDFS, used as a source and sink for MapReduce jobs. Data is split in chunks, dis- tributed and replicated among the nodes and stored on local disks. MR and HDFS daemons run on the same nodes, so the framework knows which node contains the data. Great emphasis is placed on data locality. The scheduler tries to run mappers on the same nodes that hold the input data in order to reduce network traffic during the Map phase. 26
- 45. 2.2.1 Computational Models and Extensions A few computational models for MapReduce have been proposed. Afrati and Ullman (2009) propose an I/O cost model that captures the essential features of many DISC systems. The key assumptions of the model are: • Files are replicated sets of records stored on a distributed file sys- tem with a very large block size b and can be read and written in parallel by processes; • Processes are the conventional unit of computation but have limits on I/O: a lower limit of b (the block size) and an upper limit of s, a quantity that can represent the available main memory; • Processors are the computing nodes, with a CPU, main memory and secondary storage, and are available in infinite supply. The authors present various algorithms for multiway join and sort- ing, and analyze the communication and processing costs for these ex- amples. Differently from standard MR, an algorithm in this model is a DAG of processes, in a way similar to Dryad. Additionally, the model as- sumes that keys are not delivered in sorted order to the Reduce. Because of these departures from the traditional MR paradigm, the model is not appropriate to compare real-world algorithms developed for Hadoop. Karloff et al. (2010) propose a novel theoretical model of computation for MapReduce. The authors formally define the Map and Reduce func- tions and the steps of a MR algorithm. Then they proceed to define a new algorithmic class: MRCi . An algorithm in this class is composed by a finite sequence of Map and Reduce rounds with some limitations. Given an input of size n: • each Map or Reduce is implemented by a random access machine that uses sub-linear space and polynomial time in n; • the total size of the output of each Map is less than quadratic in n; • the number of rounds is O(logi n). 27
- 46. The model makes a number of assumptions on the underlying infras- tructure to derive the definition. The number of available processors is assumed to be sub-linear. This restriction guarantees that algorithms in MRC are practical. Each processor has a sub-linear amount of memory. Given that the Reduce phase can not begin until all the Maps are done, the intermediate results must be stored temporarily in memory. This explains the space limit on the Map output which is given by the total memory available across all the machines. The authors give examples of algorithms for graph and string problems. The result of their analysis is an algorithmic design technique for MRC. A number of extensions to the base MR system have been developed. Many of these works focus on extending MR towards the database area. Yang et al. (2007) propose an extension to MR in order to simplify the implementation of relational operators. More specifically they target the implementation of join, complex, multi-table select and set operations. The normal MR workflow is extended with a third final Merge phase. This function takes as input two different key-value pair lists and outputs a third key-value pair list. The model assumes that the output of the Reduce function is fed to the Merge. The signature are as follows. Map: k1, v1 α → [ k2, v2 ]α Reduce: k2, [v2] α → k2, [v3] α Merge: k2, [v3] α , k3, [v4] β → [ k4, v5 ]γ where α, β, γ represent data lineages. The lineage is used to distinguish the source of the data, a necessary feature for joins. The signatures for the Reduce function in this extension is slightly different from the one in traditional MR. The Merge function requires its input to be organized in partitions. For this reason the Reduce function passes along the key k2 received from the Map to the next phase without modifying it. The presence of k2 guarantees that the two inputs of the Merge function can be matched by key. 28
- 47. The implementation of the Merge phase is quite complex so we refer the reader to the original paper for a detailed description. The proposed framework is efficient even though complex for the user. To implement a single join algorithm the programmer needs to write up to five different functions for the Merge phase only. Moreover, the system exposes many internal details that pollute the clean functional interface of MR. The other main area of extension is adapting MR for online analytics. This modification would give substantial benefits in adapting to changes, and the ability to process stream data. Hadoop Online Prototype (HOP) is a proposal to address this issue (Condie et al., 2009). The authors modify Hadoop in order to pipeline data between operators, and to sup- port online aggregation and continuous queries. In HOP a downstream dataflow element can begin consuming data before a producer element has completed its execution. Hence HOP can generate and refine an ap- proximate answer by using online aggregation (Hellerstein et al., 1997). Pipelining also enables to push data as it comes inside a running job, which in turn enables stream processing and continuous queries. To implement pipelining, mappers push data to reducers as soon as it is ready. The pushed data is treated as tentative to retain fault tolerance, and discarded in case of failure. Online aggregation is performed by ap- plying the Reduce function to all the pipelined data received so far. The result is a snapshot of the computation and is saved on HDFS. Continu- ous MR jobs are implemented by using both pipelining and aggregation on data streams, by reducing a sliding window of mappers output. HOP presents several shortcomings because of hybrid model. Pipelin- ing is only possible between mappers and reducers in one job. Online aggregation recomputes the snapshot from scratch each time, consum- ing computing and storage resources. Stream processing can only be performed on a window because of fault tolerance. Anyway reducers do not process the data continuously but are invoked periodically. HOP tries to transform MapReduce from a batch system to an online system by reducing the batch size and addressing the ensuing inefficiencies. HStreaming10 also provides stream processing on top of Hadoop. 10http://www.hstreaming.com 29
- 48. 2.3 Streaming Streaming is an fundamental model for computations on massive datasets (Alon et al., 1999; Henzinger et al., 1998). In the traditional streaming model we are allowed only a constant number of passes on the data and poly-logarithmic space in the size of the input n. In the semi-streaming model, we are allowed a logarithmic number of passes and O(n·polylog n) space (Feigenbaum et al., 2005). Excluding the distribution over multiple machines, these models are indeed very similar to the model of compu- tation allowed in MapReduce. Feldman et al. (2007) explore the relation- ship between streaming and MapReduce algorithms. Streaming is applicable to a wide class of data-intensive applications in which the data is modeled best as transient data streams rather than persistent relations. Examples of such applications include financial ap- plications, network monitoring, security and sensor networks. A data stream is a continuous, ordered sequence of items. However, its continuous arrival in multiple, rapid, possibly unpredictable and un- bounded streams raises new interesting challenges (Babcock et al., 2002). Data streams differ from the traditional batch model in several ways: • data elements in the stream arrive online; • the algorithm has no control over the order of the items; • streams are potentially unbounded in size; • once an item has been processed it is discarded or archived. This last fact implies that items cannot be retrieved easily unless they are explicitly stored in memory, which is usually small compared to the size of the input data streams. Processing on streams in performed via continuous queries, which are evaluated continuously as streams arrive. The answer to a continu- ous query is produced over time, always reflecting the stream items seen so far. Continuous query answers may be stored and updated as new data arrives, or they may be produced as data streams themselves. 30
- 49. Since data streams are potentially unbounded, the amount of space required to compute an exact answer to a continuous query may also grow without bound. While batch DISC systems are designed to handle massive datasets, such systems are not well suited to data stream appli- cations since they lack support for continuous queries and are typically too slow for real-time response. The data stream model is most applicable to problems where short response times are important and there are large volumes of data that are being continually produced at a high speed. New data is constantly arriving even as the old data is being processed. The amount of com- putation time per data element must be low, or else the latency of the computation will be too high and the algorithm will not be able to keep pace with the data stream. It is not always possible to produce exact answers for data stream queries by using a limited amount of memory. However, high-quality approximations are often acceptable in place of exact answers (Manku and Motwani, 2002). Sketches, random sampling and histograms are common tools employed for data summarization. Sliding windows are the standard way to perform joins and other relational operators. 2.3.1 S4 S4 (Simple Scalable Streaming System) is a distributed stream-processing engine inspired by MapReduce (Neumeyer et al., 2010). It is a general- purpose, scalable, open platform built from the ground up to process data streams as they arrive, one event at a time. It allows to easily de- velop applications for processing unbounded streams of data when a single machine cannot possibly cope with the volume of the streams. Yahoo! developed S4 to solve problems in the context of search ad- vertising with specific use cases in data mining and machine learning. The initial purpose of S4 was to process user feedback in real-time to op- timize ranking algorithms. To accomplish this purpose, search engines build machine learning models that accurately predict how users will click on ads. To improve the accuracy of click prediction the models in- 31
- 50. Processing Element Zookeeper Event Streams Coordination Events Input Events Output Business logic goes here Processing Node 1 PE PE PE PE Processing Node 2 PE PE PE PE Processing Node 3 PE PE PE PE Figure 2.3: Overview of S4. corporate recent search queries, clicks, and timing information as a form of personalization. A production system needs to process thousands of search queries per second from potentially millions of users per day. The authors initially considered extending Hadoop, but: “Rather than trying to fit a square peg into a round hole we decided to explore a programming paradigm that is simple and can operate on data streams in real-time.” S4 implements the well known Actor model (Agha, 1986). In an Actor based system, actors are the element of computation and communication is handled exclusively by message passing. Actors share no state, there- fore a system based on the Actor model lends itself to easy parallelization on a cluster of shared nothing machines. The Actor model provides en- capsulation and location transparency, thus allowing applications to be massively concurrent while exposing a simple API to developers. In the context of S4, actors are called Processing Elements (PEs) and they communicate via event streams as shown in Figure 2.3. Much like in MR, events consist of key-value pairs. Keyed data events are routed with affinity to PEs. PEs consume the events and may publish results or emit one or more events which may be consumed by other PEs. The platform instantiates a PE for each value of the key attribute. When a new key is seen in an event, S4 creates a new instance of the PE associated to that key. Thus, for each PE there will be as many instances 32
- 51. status.text:"Introducing #S4: a distributed #stream processing system" PE1 PE2 PE3 PE4 RawStatus null text="Int..." EV KEY VAL Topic topic="S4" count=1 EV KEY VAL Topic topic="stream" count=1 EV KEY VAL Topic reportKey="1" topic="S4", count=4 EV KEY VAL TopicExtractorPE (PE1) extracts hashtags from status.text TopicCountAndReportPE (PE2-3) keeps counts for each topic across all tweets. Regularly emits report event if topic count is above a configured threshold. TopicNTopicPE (PE4) keeps counts for top topics and outputs top-N topics to external persister Figure 2.4: Twitter hashtag counting in S4. as the number of different keys in the data stream. The instances are spread among the cluster to provide load balancing. Each PE consumes exactly those events whose key matches its own instantiation key. A PE is implemented by defining a ProcessEvent function. This UDF is handed the current event, can perform any kind of computation and emit new keyed events on a stream. A communication layer will take care of routing all the events to the appropriate PE. The user can define an application by specifying a DAG of PEs connected by event streams. Unlike other systems S4 has no centralized master node. Instead, it leverages ZooKeeper to achieve a clean and symmetric cluster archi- tecture where each node provides the same functionalities. This choice greatly simplifies deployments and cluster configuration changes. Figure 2.4 presents a simple example of an S4 application that keeps track of trending hashtag on Twitter. PE1 extracts the hashtags from the tweet and sends them down to PE2 and PE3 that increment their coun- ters. At regular intervals the counters are sent to an aggregator that pub- lishes the top-N most popular ones. 33
- 52. 2.4 Algorithms Data analysis researchers have seen in DISC systems the perfect tool to scale their computations to huge datasets. In the literature, there are many examples of successful applications of DISC systems in different areas of data analysis. In this section, we review some of the most signi- ficative example, with anl emphasis on Web mining and MapReduce. Information retrieval has been the classical area of application for MR Indexing bags of documents is a representative application of this field, as the original purpose of MR was to build Google’s index for Web search. Starting from the original algorithm, many improvements have been proposed, from single-pass indexing to tuning the scalability and efficiency of the process. (McCreadie et al., 2009a,b, 2011). Several information retrieval systems have been built on top of MR. Terrier (Ounis et al., 2006), Ivory (Lin et al., 2009) and MIREX (Hiemstra and Hauff, 2010) enable testing new IR techniques in a distributed set- ting with massive datasets. These systems also provide state-of-the-art implementation of common indexing and retrieval functionalities. As we explain in Chapter 3, pairwise document similarity is a com- mon tool for a variety of problems such as clustering and cross-document coreference resolution. MR algorithms for closely related problems like fuzzy joins (Afrati et al., 2011a) and pairwise semantic similarity (Pan- tel et al., 2009) have been proposed. Traditional two-way and multiway joins have been explored by Afrati and Ullman (2010, 2011) Logs are a gold mine of information about users’ preferences, natu- rally modeled as bags of lines. For instance frequent itemset mining of query logs is commonly used for query recommendation. Li et al. (2008) propose a massively parallel algorithm for this task. Zhou et al. (2009) design a DISC-based OLAP system for query logs that supports a vari- ety of data mining applications. Blanas et al. (2010) study several MR join algorithms for log processing, where the size of the bags is very skewed. MapReduce has proven itself as an extremely flexible tool for a num- ber of tasks in text mining such as expectation maximization (EM) and latent dirichlet allocation (LDA) (Lin and Dyer, 2010; Liu et al., 2011). 34
- 53. Mining massive graphs is another area of research where MapReduce has been extensively employed. Cohen (2009) presents basic patterns of computation for graph algorithms in MR, while Lin and Schatz (2010) presents more advanced performance optimizations. Kang et al. (2011) propose an algorithm to estimate the graph diameter for graphs with billions of nodes like the Web, which is by itself a challenging task. Frequently computed metrics such as the clustering coefficient and the transitivity ratio involve counting triangles in the graph. Tsourakakis et al. (2009) and Pagh and Tsourakakis (2011) propose two approaches for approximated triangle counting on MR using randomization, while Yoon and Kim (2011) propose an improved sampling scheme. Suri and Vassilvitskii (2011) propose exact algorithms for triangle counting that scale to massive graphs on MapReduce. MR has been used also to address NP-complete problems. Brocheler et al. (2010) and Afrati et al. (2011b) propose algorithms for subgraph matching. Chierichetti et al. (2010) tackles the problem of max cover- ing, which can be applied to vertexes and edges in a graph. Lattanzi et al. (2011) propose a filtering technique for graph matching tailored for MapReduce. In Chapter 4 we will present two MapReduce algorithms for graph b-matching with applications to social media. A number of different graph mining tasks can be unified via general- ization of matrix operations. Starting from this observation, Kang et al. (2009) build a MR library for operation like PageRank, random walks with restart and finding connected components. Co-clustering is the si- multaneous clustering of the rows and columns of a matrix in order to find correlated sub-matrixes. Papadimitriou and Sun (2008) describe a MR implementation called Dis-Co. Liu et al. (2010) explore the problem of non-negative matrix factorization of Web data in MR. Streaming on DISC system is still an unexplored area of research. Large scale general purpose stream processing platforms are a recent de- velopment. However, many streaming algorithms in the literature can be adapted easily. For an overview of distributed stream mining algo- rithms see the book by Aggarwal (2007). For large scale stream mining algorithms see Chapter 4 of the book by Rajaraman and Ullman (2010). 35
- 54. DISC technologies have also been applied to other fields, such as sci- entific simulations of earthquakes (Chen and Schlosser, 2008), collabo- rative Web filtering (Noll and Meinel, 2008) and bioinformatics (Schatz, 2009). Machine learning has been a fertile ground for MR applications such as prediction of user rating of movies (Chen and Schlosser, 2008). In general, many widely used machine learning algorithms can be im- plemented in MR (Chu et al., 2006). 36
- 55. Chapter 3 Similarity Self-Join in MapReduce Similarity self-join computes all pairs of objects in a collection such that their similarity value satisfies a given criterion. For example it can be used to find similar users in a community or similar images in a set. In this thesis we focus on bags of Web pages. The inherent sparseness of the lexicon of pages on the Web allows for effective pruning strategies that greatly reduce the number of pairs to evaluate. In this chapter we introduce SSJ-2 and SSJ-2R, two novel parallel al- gorithms for the MapReduce framework. Our work builds on state of the art pruning techniques employed in serial algorithms for similarity join. SSJ-2 and SSJ-2R leverage the presence of a distributed file system to support communication patterns that do not fit naturally the MapRe- duce framework. SSJ-2R shows how to effectively utilize the sorting facilities offered by MapReduce in order to build a streaming algorithm. Finally, we introduce a partitioning strategy that allows to avoid memory bottlenecks by arbitrarily reducing the memory footprint of SSJ-2R. We present a theoretical and empirical analysis of the performance of our two proposed algorithms across the three phases of MapReduce. Experimental evidence on real world data from the Web demonstrates that SSJ-2R outperforms the state of the art by a factor of 4.5. 37
- 56. 3.1 Introduction In this chapter, we address the similarity self-join problem: given a col- lection of objects, we aim at discovering every pair of objects with high similarity, according to some similarity function. The task of discovering similar objects within a given collection is common to many real world data mining and machine learning problems. Item-based and user-based recommendation algorithms require to com- pute, respectively, pair-wise similarity among users or items. Due to the large number of users and objects commonly handled by popular recom- mender systems similarity scores are usually computed off-line. Near duplicate detection is commonly performed as a pre-processing step before building a document index. It may be used to detect redun- dant documents, which can therefore be removed, or it may be a hint to discover content farms and spam websites exploiting content repurpos- ing strategies. Near duplicate detection finds application also in the area of copyright protection as a tool for discovering plagiarism. Density-based clustering algorithms like DBSCAN (Ester et al., 1996) or OPTICS (Ankerst et al., 1999) inherently join the input data based on similarity relationships. Correlation clustering (Bansal et al., 2004) uses similarity relationship between the objects instead of the actual repre- sentation of the objects. All these algorithms will draw high benefit from efficient and scalable MapReduce implementations of similarity joins. Finding similar objects is also a basic step for data cleaning tasks. When dealing with real world data, we wish to normalize different but simi- lar representations of the same entity, e.g. different names or addresses, caused by mistakes or formatting conventions. Similarity joins also play an important role in distance-based outlier detection. We focus on document collections and model them as bags of vectors (see Section 1.2.1). Each document is a vector in a highly-dimensional space. Documents are a particular kind of data that exhibits a significant sparseness: only a small subset of the whole lexicon occurs in any given document. This sparsity allows to exploit pruning strategies that reduce the potentially quadratic number of candidate pairs to evaluate. 38
- 57. Finally, the size of the collection at hand poses new interesting chal- lenges. This is particularly relevant for Web-related collections, where the number of documents involved is measured in billions. For this set- ting, distributed solutions become mandatory. Indeed, there are a few related proposals that exploit the MapReduce framework. Elsayed et al. (2008) propose a MapReduce algorithm to compute the similarity be- tween every pair of documents in a collection, without taking advantage of any pruning strategy. Vernica et al. (2010) present a MapReduce algo- rithm to compute the similarity join of collections of sets. Our main contributions are the following. • We present SSJ-2 and SSJ-2R the efficient distributed algorithms based on the MapReduce framework to compute the similarity self- join on a collection of documents. • We borrow from existing pruning techniques designed for serial algorithms, and we extend them to the distributed setting. • We exploit selective communication patterns that do not naturally fit the MapReduce paradigm. • We provide detailed analytical and empirical analysis of the algo- rithms across the various phases of the MapReduce framework. • We show that SSJ-2R performs nicely on a sample of the WT10g TREC Web Corpus.1 The rest of the chapter is organized as follows. In Section 3.2 we in- troduce the similarity self-join problem and some solutions adopted by non-parallel algorithms. In Section 3.3 we discuss the algorithms for sim- ilarity self-join that are based on the MapReduce framework. Section 3.4 presents our proposed algorithms, which are theoretically analyzed in Section 3.5 and experimentally evaluated in Section 3.6. 1http://ir.dcs.gla.ac.uk/test_collections/wt10g.html 39
- 58. 3.2 Problem definition and preliminaries We address the similarity self-join problem applied to a collection D of documents. Let L be the lexicon of the collection. Each document d is represented as a |L|-dimensional vector. Without loss of generality, we assume that documents are normalized, so d[i] denotes the number of occurrences of the i-th term in the document d divided by the norm d . We adopt the cosine distance to measure the similarity between two doc- uments. For normalized documents the cosine similarity can be simply computed as the inner product between document vectors. Problem 1 (Similarity Self-Join Problem). Given a collection of normalized document-vectors D = {d1, . . . , dN }, a similarity function σ: D×D → R and a minimum similarity threshold σ, the Similarity Self-Join problem requires to discover all those pairs di, dj ∈ D with similarity above the threshold: σ(di, dj) = 0≤t<|L| di[t] · dj[t] ≥ σ Note that the results discussed in this chapter can be easily applied to other similarity measures, such as Jaccard, Dice or overlap. Differently from normal join problems, self-join involves joining a large table with itself. Thus it is not possible to apply traditional algo- rithms for data warehousing, that join a large fact table with smaller di- mension tables. Recent algorithms for log processing in MR also assume that one of the tables is much smaller that the other (Blanas et al., 2010). Following Arasu et al. (2006); Xiao et al. (2009), we classify algorithms for similarity self-join by their solution to the following sub-problems: 1. Signature scheme: a compact representation of each document; 2. Candidate generation: identifying potentially similar document pairs given their signature; 3. Verification: computing document similarity; 4. Indexing: data structures for speeding up candidate generation and verification. 40
- 59. The naïve approach produces the document itself as the signature. It generates all the O(N2 ) possible document-signature pairs, and com- putes their actual similarity without any supporting indexing structure. This approach is overly expensive in the presence of sparse data such as bag of documents. It is very common to have documents thad to not share any term, leading to a similarity of zero. In this case, smart pruning strategies can be exploited to discard early such document pairs. Broder et al. (1997) adopt a simple signature scheme, that we refer to as Term-Filtering. The signature of a document is given by the terms occurring in that document. These signatures are stored in an inverted index, which is then used to compare only pairs of documents sharing at least one item in their signature, i.e. one term. Prefix-Filtering (Chaudhuri et al., 2006) is an extension of the Term- Filtering idea. Let ˆd be an artificial document such that ˆd[t] = maxd∈D d[t]. Given a document d, let its boundary b(d) be the largest integer such that 0≤t<b(d) d[t] · ˆd[t] < σ. The signature of the document d is the set of terms occurring in the document vector beginning from position b(d), S(d) = {b(d) ≤ t < |L| | d[t] = 0}. It is easy to show that if the signatures of two documents di, dj have empty intersection, then the two docu- ments have similarity below the threshold. Without loss of generality let us assume that b(di) b(dj). (S(di) ∩ S(dj) = ∅) ⇒ b(di)≤t<|L| di[t] · dj[t] = 0 ⇒ σ(di, dj) = 0≤t<b(di) di[t] · dj[t] ≤ 0≤t<b(di) di[t] · ˆd[t] < σ Therefore, only document signatures are stored in the inverted index and later used to generate candidate document pairs. Eventually, the full documents need to be retrieved in order to compute the actual similarity. This technique was initially proposed for set-similarity joins and later extended to documents with real-valued vectors. In particular, Bayardo et al. (2007) adopt an online indexing and match- ing approach. Index generation, candidate pair generation and similarity score computation are all performed simultaneously and incrementally. 41
- 60. Each document is matched against the current index to find potential candidates. The similarity scores are computed by retrieving the candi- date documents directly from the collection. Finally, a signature is ex- tracted from the current document and added to the index. This approach results in a single full scan of the input data, a small number of random accesses to single documents, and a smaller (on av- erage) index to be queried. Prefix-filtering outperforms alternative tech- niques such as LSH (Gionis et al., 1999), PartEnum (Arasu et al., 2006) and ProbeCount-Sort (Sarawagi and Kirpal, 2004), which we therefore do not considered in our work. Unfortunately, an incremental approach that leverages a global shared index is not practical on a large parallel system because of contention on the shared resource. Finally, Xiao et al. (2008) present some additional pruning techniques based on positional and suffix information. However these techniques are specifically tailored for set-similarity joins and cannot be directly ap- plied to document similarity. 3.3 Related work In this section we describe two MR algorithm for the similarity self-join problem. Each exploits one of the pruning techniques discussed above. 3.3.1 MapReduce Term-Filtering (ELSA) Elsayed et al. (2008) present a MapReduce implementation of the Term- Filtering method. Hereafter we refer to it as ELSA for convenience. The authors propose an algorithm for computing the similarity of every doc- ument pair, which can be easily adapted to our setting by adding a sim- ple post-filtering. The algorithm runs two consecutive MR jobs, the first builds an inverted index and the second computes the similarities. Indexing: Given a document di, for each term, the mapper emits the term as the key, and a tuple i, di[t] consisting of document ID and weight as the value. The shuffle phase of MR groups these tuples by term and delivers these inverted lists to the reducers, that write them to disk. 42
- 61. Map: i, di → [ t, i, di[t] | di[t] > 0] Reduce: t, [ i, di[t] , j, dj[t] , . . .] → [ t, [ i, di[t] , j, dj[t] , . . .] ] Similarity: Given the inverted list of term t, the mapper produces the contribution wij[t] = di[t] · dj[t] for every pair of documents where the term t co-occurs. This value is associated with a key consisting of the pair of document IDs i, j . For any document pair the shuffle phase will pass to the reducer the contribution list Wij = {wij[t] | wij[t] > 0, ∀t ∈ L} from the various terms, which simply need to be summed up. Map: t, [ i, di[t] , j, dj[t] , . . .] → [ i, j , wij[t] ] Reduce: i, j , Wij → i, j , σ(di, dj) = w∈Wij w The Term-Filtering is exploited implicitly: the similarity of two doc- uments that do not share any term is never evaluated because none of their terms ever occurs in the same inverted list. The main drawback of this approach is caused by the large number of candidate document pairs that it generates. In fact, there are many document pairs that share only a few terms but have anyway a simi- larity largely below the threshold. The number of candidates directly affects completion time. More importantly it determines the shuffle size, the volume of intermediate data to be moved from mappers to reducers. Minimizing shuffle size is critical because network bandwidth is the only resource that cannot be easily added to a cluster. Finally, recall that reducers may start only after every mapper has completed. Therefore, the presence of a few long inverted lists for com- mon terms induces a significant load imbalance. Most of the resources will remain idle until the processing of the longest inverted list is com- pleted. To alleviate this issue Elsayed et al. remove the top 1% most fre- quent terms, thus trading efficiency for precision. Our goal is to provide an efficient algorithm that computes the exact similarity. 43
- 62. Figure 3.1 illustrates an example of how ELSA works. For ease of explanation, the document vectors are not normalized. Term-Filtering avoids computing similarity scores of documents that do not share any term. For the special case in which an inverted list contains only one doc- ument, the similarity Map function does not produce any output. The two main problems of ELSA result evident from looking at this image. First, long inverted lists may produce a load imbalance and slow down the algorithm considerably, as for term “B” in the figure. Second, the algorithm computes low similarity scores which are not useful for the typical applications, as for document pair d1, d2 in the figure. shuffle map map map map shuffle <B, [(d1,1), (d2,1), (d3,2)]> <C, [(d1,1), (d3,1)]> <D, [(d2,2)]> <A, [(d1,2), (d3,1)]> <A, (d1,2)> <B, (d1,1)> <C, (d1,1)> <B, (d2,1)> <D, (d2,2)> <A, (d3,1)> <B, (d3,2)> <C, (d3,1)> <B, [(d1,1), (d2,1), (d3,2)]> <A, [(d1,2), (d3,1)]> <C, [(d1,1), (d3,1)]> <D, [(d2,2)]> reduce reduce reduce reduce Indexing Similarity <(d1,d2), 1> <(d1,d3), 2> <(d2,d3), 2> <(d1,d3), 1> <(d1,d3), 2> <(d1,d3), [2,2,1]> <(d1,d2), [1]> <(d2,d3), [2]> reduce reduce reduce <(d1,d3), 5> <(d1,d2), 1> <(d2,d3), 2> mapd1 "A A B C" mapd3 "A B B C" mapd2 "B D D" Figure 3.1: ELSA example. 3.3.2 MapReduce Prefix-Filtering (VERN) Vernica et al. (2010) present a MapReduce algorithm based on Prefix- Filtering that uses only one MR step. Indeed, the authors discuss several algorithm for set-similarity join operations. Here we describe the best performing variant for set-similarity self-join. Hereafter we refer to it as VERN for convenience. For each term in the signature of a document t ∈ S(di) as defined by Prefix-Filtering, the map function outputs a tuple with key the term t itself and value the whole document di. The shuffle phase delivers to each reducer a small sub-collection of documents that share at least one term in their signatures. This process can be thought as the creation of an inverted index of the signatures, where each post- ing is the document itself rather than a simple ID. Finally, each reducer 44
- 63. finds similar pairs among candidates by using state-of-the-art serial algo- rithms (Xiao et al., 2008). The Map and Reduce functions are as follows. Map: i, di → [ t, di | t ∈ S(di)] Reduce: t, Dv = [di, dj, . . .] → [ i, j , σ(di, dj) | di, dj ∈ Dv] Nonetheless, this approach does not bring a significant improvement over the previous strategy. First, a document with a signature of length n is replicated n times, even if there are no other documents with an overlapping signature. Second, pairs of similar documents that have m common terms in their signatures are produced m times at different re- ducers. Computing these duplicates is a overhead of parallelization, and their presence requires a second scan of the output to get rid of them. Figure 3.2 illustrates an example run of VERN. Light gray terms are pruned from the document by using Prefix-Filtering. Each document is replicated once for each non-pruned term it contains. Finally, the reducer computes the similarity of the bag of documents it receives by employ- ing a serial SSJ algorithm. As shown in Figure 3.2, VERN computes the similarity of the pair d1, d3 multiple times at different reducers. We propose here a simple strategy that solves the issue of duplicate similarity computation. We use this modified version of the original VERN algorithm in our evaluation. This modified version runs slightly but consistently faster than the original one, and it does not require post- processing. The duplicate similarities come from pair of documents that share more than one term in their signatures. Let Sij = S(di) ∩ S(dj) be the set of such shared terms in document pair di, dj . Let ˆt be the last of such terms in the order imposed to the lexicon by Prefix-Filtering ˆt = tx | tx ty ∀ tx, ty ∈ Sij. The reducer that receives each pair can simply check if its key corresponds to ˆt and compute the similarity only in this case. The term ˆt for each pair of documents can be efficiently com- puted by a simple backwards scan of the two arrays that represent the documents. This strategy allows to avoid computing duplicate similari- ties and does not impose any additional overhead the original algorithm. 45
- 64. shuffle <(d1,d3), 5> <(d1,d3), 5> <A, (d1, A A B C)> <B, (d1, A A B C)> <C, (d1, A A B C)> <D, (d2, B D D)> <B, (d3, A B B C)> <C, (d3, A B B C)> mapd1 "A A B C" mapd2 "B D D" mapd3 "A B B C" <B, [(d1, A A B C), (d3, A B B C)]> <A, (d1, A A B C)> <C, [(d1, A A B C), (d3, A B B C)]> <D, [(d2, B D D)]> reduce reduce reduce reduce Figure 3.2: VERN example. 3.4 SSJ Algorithms In this section we describe two algorithms based on Prefix-Filtering that overcome the weak points of the algorithms presented above. The first algorithm, named SSJ-2, performs a Prefix-Filtering in two MR steps. Note that in the first step we use a naïve indexing algorithm but if needed more advanced techniques can be used (McCreadie et al., 2009b, 2011). The second algorithm, named SSJ-2R, additionally uses a remainder file to broadcast data that is likely to be used by every reducer. It also effec- tively partitions the search space to reduce the memory footprint. Code for both algorithm is open source and available online.2 3.4.1 Double-Pass MapReduce Prefix-Filtering (SSJ-2) This algorithm is and extention of ELSA, and also consists of an indexing phase followed by a similarity computation phase. SSJ-2 shortens the inverted lists by employing Prefix-Filtering. As shown in Figure 3.3, the effect of Prefix-Filtering is to reduce the portion of document indexed. The terms occurring in di up to position b(di), or bi for short, need not be indexed. By sorting terms in decreasing order of frequency, the most frequent terms are discarded. This pruning shortens the longest inverted lists and brings a significant performance gain. 2https://github.com/azaroth/Similarity-Self-Join 46
- 65. To improve load balancing we employ a simple bucketing technique During the indexing phase we randomly hash the inverted lists to differ- ent buckets. This spreads the longest lists uniformly among the buckets. Each bucket is then consumed by a different mapper in the next phase. Pruned Indexed Pruned Indexed di dj bi bj |L|0 Figure 3.3: Pruned document pair: the left part (orange/light) has been pruned, the right part (blue/dark) has been indexed. Unfortunately with this schema the reducers do not have enough in- formation to compute the similarity between di and dj. They receive only the contribution from terms t bj, assuming bi bj. For this reason, the reducers need two additional remote I/O operations to retrieve the two documents di and dj from the underlying distributed file system. SSJ-2 improves over both ELSA and VERN in terms of the amount of intermediate data produced. Thanks to Prefix-Filtering, the inverted lists are shorter than in ELSA and therefore the number of candidate pairs generated decreases quadratically. In VERN each document is al- ways sent to a number of reducers equal to the size of its signature, even if no other document signature shares any term with it. In SSJ-2 a pair 47
- 66. of documents is sent to the reducer only if they share at least one term in their signature. Furthermore, while SSJ-2 computes the similarity be- tween any two given documents just once, VERN computes the similarity of two documents in as many reducers as the size of the intersection of their signatures. Therefore, SSJ-2 has no computational overhead due to parallelization, and significantly reduces communication costs. Figure 3.4 presents an example for SSJ-2. As before, light gray terms have been pruned and documents are not normalized to ease the expla- nation. Pairs of documents that are below the similarity threshold are discarded early. However the reducer of the similarity phase needs to access the remote file system to retrieve the documents in order to com- pute the correct final similarity score. shuffle <(d1,d3), 2> <(d1,d3), 1> <(d1,d3), [2,1]> reduce <(d1,d3), 5> HDFS d3 "A B B C" d1 "A A B C" Similarity map map map shuffle <B, [(d1,1), (d3,2)]> <C, [(d1,1), (d3,1)]> <D, [(d2,2)]> <B, (d1,1)> <C, (d1,1)> <D, (d2,2)> <B, (d3,2)> <C, (d3,1)> mapd1 "A A B C" mapd2 "B D D" mapd3 "A B B C" <B, [(d1,1), (d3,2)]> <C, [(d1,1), (d3,1)]> <D, [(d2,2)]> reduce reduce reduce Indexing Figure 3.4: SSJ-2 example. 48
- 67. 3.4.2 Double-Pass MapReduce Prefix-Filtering with Re- mainder File (SSJ-2R) For any given pair of documents di, dj , the reducers of SSJ-2 receive only partial information. Therefore, they need to retrieve the full docu- ments in order to correctly compute their similarity. Since a node runs multiple reducers over time, each of them remotely accessing two doc- uments, in the worst case this is equivalent to broadcasting the full col- lection to every node, with obvious limitations to the scalability of the algorithm. We thus propose an improved algorithm named SSJ-2R that does not perform any remote random access, and that leverages the non- indexed portion of the documents. Let us make a few interesting observations. First, some of the terms are very common, and therefore used to compute the similarity of most document pairs. For those terms, it would be more efficient to broad- cast their contributions rather than pushing them through the MR frame- work. Indeed, such piece of information is the one pruned via Prefix- Filtering during the indexing phase. We thus propose to store the pruned portion of each document in a remainder file DR, which can be later re- trieved by each reducer from the underlying distributed file system. Second, the remainder file DR does not contain all the information needed to compute the final similarity. Consider Figure 3.3, each reducer receives the contributions wij[t] = di[t] · dj[t] | t bj. DR contains in- formation about the terms di[t] | t bi} and {dj[t] | t bj. But, subtly, no information is available for those terms di[t] | bi t bj. On the one hand, those term weights are not in the remainder file because they have been indexed. On the other hand, the corresponding inverted lists contain the frequency of the terms in di but not of those occurring in dj, and therefore, the weights wij[t] = di[t] · dj[t] cannot be produced. We thus propose to let one of the two documents be delivered to the reducer through the MR framework by shuffling it together with the weights of the document pairs. Given two documents di and dj as shown in Figure 3.3, if bi bj we call di the Least Pruned Document and dj the Most Pruned Document. Our goal is to group at the reducer each docu- 49
- 68. ment d with the contributions w of every document pair di, dj for which d is the least pruned document between di and dj. This document con- tains the pieces of information that we are missing in order to compute the final similarity score. This can be achieved by properly defining the keys produced by the mappers and their sorting and grouping operators. More formally, we define two functions LPD(di, dj) and MPD(di, dj). LPD(di, dj) = i, if bi bj j, otherwise MPD(di, dj) = j, if bi bj i, otherwise First, we slightly modify the similarity Map function such that for ev- ery document pair of the given inverted list, it produces as keys a couple of document IDs where the first is always the LPD, and as values the MPD and the usual weight w. Map: [ t, [ i, di[t] , j, dj[t] , . . .] ] → [ LPD(di, dj), MPD(di, dj) , MPD(di, dj), wij[t] ] Second, we take advantage of the possibility of running independent Map functions whose outputs are then shuffled together. We define a Map function that takes the input collection and outputs its documents. Map: i, di → [ i, φ , di ] where φ is a special value such that φ < i ∀di ∈ D. Third, we make use of the possibility offered by Hadoop to rede- fine parts of its communication pattern. The process we describe here is commonly known as secondary sort in MR parlance. We redefine the key partitioning function, which selects which reducer will process the key. Our function takes into account only the first document ID in the key. This partitioning scheme guarantees that all the key-value pairs that share the same LPD will end up in the same partition, together with one copy of the LPD document itself coming from the second Map function. We instruct the shuffle phase of MR to sort the keys in each partition in ascending order. This order takes into account both IDs, the first as primary key and the second as secondary key. Consequently, for each 50
- 69. document di MR builds a list of key-value pairs such that the first key is i, φ , followed by every pair of document IDs for which di is the LPD. Finally, we override the grouping function, which determines whether two keys belong to the same equivalence class. If two keys are equiva- lent, their associated values will be processed by the same single call to the Reduce function. Concretely, the grouping function builds the argu- ment list for a call to the Reduce function by selecting values from the partition such that the corresponding keys are equivalent. Therefore our grouping function must consistent with our partitioning scheme: two keys i, j and i , j are equivalent iff i = i . The input of the Reduce function is thus as follows. i, φ , [di, j, wij[t ] , j, wij[t ] , . . . , k, wik[t ] , k, wik[t ] , . . .] The key is just the first key in the group, as they are all equivalent to MR. The first value is the LPD document di. Thanks to the sorting of the keys, it is followed by a set of contiguous stripes of weights. Each stripe is associated to the same document dj | j = MPD(di, dj). SSJ-2R can now compute the similarity σ(di, dj) in one pass. Before the algorithm starts, each reducer loads the remainder file DR in mem- ory. For each Reduce call, SSJ-2R starts by caching di, which is at the beginning of the list of values. Then, for each dj in the list, it sums up all the corresponding weights wij to compute a partial similarity. Finally, it retrieves the pruned portion of dj from DR, computes the similarity of di to the pruned portion of dj and adds this to the partial similarity com- puted before. This two step process correctly computes the final similar- ity σ(di, dj) because all the terms bi t bj are available both in di and in the pruned portion of dj. This process is repeated for each stripe of weights belonging to the same document pair in the list of values. Differently from SSJ-2, SSJ-2R performs no remote access to the doc- ument collection. Given a document pair, one is delivered fully through the MapReduce framework, and the other is partially retrieved from the remainder file DR. The advantage in terms of communication costs is given by the remainder file. Indeed, DR is much smaller than the input collection. We show experimentally that its size is one order of magni- 51
- 70. tude smaller than the input. Therefore, DR can be efficiently broadcast to every node through the distributed file system. Each reducer can load it in main memory so that the similarity computation can be fully accom- plished without any additional disk access. Figure 3.5 illustrates the full data flow of SSJ-2R with an example. As before, light gray terms have been pruned and documents are not nor- malized. SSJ-2R stores the pruned part of each document in the remain- der file, which is put in the distributed cache in order to be broadcast. The reducer of the similarity phase reads the remainder file in memory before starting to process its value list. In the example, d1 is delivered through the MR framework, while the pruned part of d3 is recovered from the remainder file. This procedure allows to correctly compute the contributions of the term “A” which was pruned from the documents. The contributions from terms “B” and “C” are computed by the mapper of the similarity phase and delivered normally through MR. 3.4.3 Partitioning Even though the remainder file DR is much smaller than the original col- lection, its size will grow when increasing the collection size, and there- fore it may hinder the scalability of the algorithm. To overcome this issue, we introduce a partitioning scheme for the remainder file. Given a user defined parameter K, we split the range of document identifiers into K equally sized chunks, so that the unindexed portion of document di falls into the i/K -th chunk. Consequently, we modify the partitioning function which maps a key emitted by the map- per to a reducer. We map each key i, j to the j/K -th reducer instance, i.e. the mapping is done on the basis of the MPD. This means that each reducer will receive only weights associated to a portion of the document space. Therefore, the reducer needs to retrieve and load in memory only 1/K-th of the remainder file DR. This new partitioning scheme spreads the weights associated to the same LPD document over K different reducers. Therefore, to correctly compute the final similarity SSJ-2R needs a copy of the LPD document 52
- 71. shuffle <B, [(d1,1), (d3,2)]> <C, [(d1,1), (d3,1)]> <D, [(d2,2)]> <B, (d1,1)> <C, (d1,1)> <D, (d2,2)> <B, (d3,2)> <C, (d3,1)> mapd1 "A A B C" mapd2 "B D D" mapd3 "A B B C" <B, [(d1,1), (d3,2)]> <C, [(d1,1), (d3,1)]> <D, [(d2,2)]> reduce reduce reduce Indexing shuffle <(d1,d3), 2> <(d1,d3), 1> <(d1,✦),"A A B C"> <(d1,d3), 2> <(d1,d3), 1> reduce <(d1,d3), 5> Similarity map map map map Remainder File d1 "A A" d3 "A" d2 "B" Distributed Cache <(d1,✦), "A A B C"> <(d3,✦), "A B B C"> Figure 3.5: SSJ-2R example. di at each of these reducers. For this reason, we replicate K times the special key i, φ and its associated value di, once for each partition. The parameter K allows to tune the memory usage of SSJ-2R and controls the tradeoff with the communication cost due to replication. 3.5 Complexity analysis In Section 2.2.1 we presented a few proposals for modeling MapReduce algorithms (Afrati and Ullman, 2009; Karloff et al., 2010). Indeed, esti- mating the cost of a MapReduce algorithm is quite difficult, because of 53
- 72. Table 3.1: Symbols and quantities. Symbol Description d d Avg. and Max. document length s s Avg. and Max. signature length p p Avg. and Max. inverted list length with Prefix-Filtering l Avg. inverted list length without pruning r Cost of a remote access to a document R Cost of retrieving the remainder file DR Table 3.2: Complexity analysis. ALGORITHM Map Shuffle Reduce ELSA l2 |L| · l 2 d VERN s · d |D| · s · d p2 · d SSJ-2 p2 |L| · p2 d + r SSJ-2R p2 |L| · p2 + |D| · d + R d the inherent parallelism, the hidden cost of the shuffling phase, the over- lap among computation and communication managed implicitly by the framework, the non-determinism introduced by combiners and so on. We prefer to model separately the three main steps of a MapReduce jobs: the Map and Reduce functions, and the volume of the data to be shuffled. In particular, we take into consideration the cost associated to the function instance with the largest input. This way, we roughly estimate the maximum possible degree of parallelism and we are able to compare the different algorithms in deeper detail. We refer to Table 3.1 for the symbols used in this section. The quantity l can also be seen as the average frequency of the terms in the lexicon L. Similarly, p can also be seen as the number of signatures containing any given term. Clearly, it holds that p ≤ l. The running time of ELSA is dominated by the similarity phase. Its 54
- 73. Map function generates every possible document pair for each inverted list, with a cost of O(l2 ). Most of this large number of candidate pairs has a similarity below the threshold. Furthermore, the presence of long inverted lists introduces stragglers. Since reducers may start only after every mapper has completed, mappers processing the longest lists keep resources waiting idly. Since the shuffling step handles a single datum for every generated pair, we can estimate the cost by summing over the various inverted lists as O(|L|·l 2 ). The Reduce function just sums up the contributions of the various terms, with a cost O(d). VERN runs only one MR job. The Map replicates each document d |S(d)| times, with a cost of O(s · d). Similarly, we can estimate the shuffle size as O(|D| · d · s). The Reduce evaluates the similarity of every pair of documents in its input, with cost O(p2 · d). Due to Prefix-Filtering, the maximum reducer input size is p, which is smaller than l. By comparing the two algorithms, we notice the superiority of VERN in the first two phases of the computation. The Map function generates a number of replicas of each document, rather then producing a quadratic number of partial contributions. Considering that |L|·l is equal to |D|·d, and that l is likely to be much larger than s, it is clear that ELSA has the largest shuffle size. Conversely, the Reduce cost for VERN is quadratic in the size of the pruned lists p. Our proposed algorithms SSJ-2 and SSJ-2R have a structure simi- lar to ELSA. The Map cost O(p2 ) depends on the pruned inverted lists. For SSJ-2R, we are disregarding the cost of creating replicas of the input in the similarity Map function, since it is much cheaper than processing the longest inverted list. They have similar shuffles sizes, respectively O(|L| · p2 ) and O(|L| · p2 + |D| · d + R). In this case we need to con- sidered the cost of shuffling the input documents and the remainder file generated by SSJ-2R. Note that we are considering the remainder file as a shuffle cost even though it is not handled by MapReduce. Finally, the Reduce cost is different. In addition to the contributions coming from the pruned inverted index, SSJ-2 needs to access documents remotely with a total cost of O(d + r). Conversely SSJ-2R has a cost of O(d) since the unindexed portion of the document is already loaded in memory at 55
- 74. the local node, delivered via the distributed file system. Thanks to Prefix-Filtering, the Map cost of our proposed algorithm smaller than ELSA, yet larger than VERN. For the same reason, the shuf- fle size of SSJ-2 is smaller than ELSA but still larger than VERN, if we assume that p is not significantly smaller than l. For SSJ-2R, the shuffle size is probably its weakest point. Shuffling the whole collection within the MapReduce data flow increases the volume of intermediate data. The Reduce function of SSJ-2 needs to remotely recover the documents be- ing processed to retrieve their unindexed portions. This dramatically increases its cost beyond ELSA but can hardly be compared with VERN. SSJ-2R has about the same cost as ELSA when assuming that the remain- der file is already loaded in memory. It is difficult to combine the costs of the various phases of the four algorithms. Therefore, it is not possible to understand which is the best. We can conclude that Elsayed et al. is the worst of the four, due to the non exploitation of the Prefix-Filtering, and that the impact of the shuffling phase will determine the goodness of our proposed algorithms. In the experimental section, we evaluate empirically the efficiency of the four algorithms in the three steps of the MapReduce framework. 3.6 Experimental evaluation In this section we describe the performance evaluation of the algorithms. We used several subsets of the TREC WT10G Web corpus. The original dataset has 1,692,096 english language documents. The size of the entire uncompressed collection is around 10GiB. In Table 3.3 we describe the samples of the collection we used, ranging from ∼ 17k to ∼ 63k docu- ments. We preprocessed the data to prepare it for analysis. We parsed the dataset stripping HTML, removed stop-words, performed stemming and vectorization of the input and extracted the lexicon. We also sorted the features inside each document in decreasing order of term frequency in order to effectively utilize Prefix-Filtering. We ran the experiments on a 5-node cluster. Each node was equipped with two Intel Xeon E5520 CPUs @2.27GHz, with 8 virtual cores (for a 56
- 75. Table 3.3: Samples from the TREC WT10G collection. D17K D30K D63K # documents 17,024 30,683 63,126 # terms 183,467 297,227 580,915 # all pairs 289,816,576 941,446,489 3,984,891,876 # similar pairs 94,220 138,816 189,969 total of 80 virtual cores), a 2TiB disk, 8GiB of RAM, and Gigabit Ethernet. We used one of the nodes to run Hadoop’s master daemons (NameN- ode and JobTracker), the rest were configured as slaves running DataN- ode and TaskTracker daemons. Two of the virtual cores on each slave machine were reserved to run the daemons, the rest were equally split among map and reduce slots (7 each), for a total of 28 slots for each phase. We tuned Hadoop’s configuration as follows: we allocated 1GiB of memory to each daemon and 400MiB to each task, changed the block size of HDFS to 256MiB and the file buffer size to 128KiB, disabled spec- ulative execution and enabled JVM reuse and map output compression. For each algorithm, we wrote an appropriate combiner to reduce the shuffle size (a combiner is a reduce-like function that runs inside the mapper to aggregate partial results). For SSJ-2 and SSJ-2R the combiner perform the sums of partial scores in the values, according to the same logic used in the reducer. We also implemented raw comparators for ev- ery key type used in order to get better performance (raw comparators compare keys during sorting without deserializing them into objects). 3.6.1 Running time We compared the four algorithms described in the previous sections. The two baselines ELSA and VERN and the two algorithms proposed by us: SSJ-2 and SSJ-2R. VERN would require an additional step for removing duplicate similar pairs. We did not need to implement this step thanks to the strategy described in Section 3.3.2 Therefore our analysis does not take into account the overhead induced by such duplicate removal. For SSJ-2R we used a partitioning factor of the remainder file K = 4. 57
- 76. 0 10000 20000 30000 40000 50000 60000 15000 20000 25000 30000 35000 40000 45000 50000 55000 60000 65000 Time(seconds) Number of vectors ELSA VERN SSJ-2 SSJ-2R Figure 3.6: Running time. We enabled partitioning just for the sake of completeness, given that the mappers were not even close to fill the available memory. We use 56 mappers and 28 reducers, so that the mappers finish in two waves and all the reducers can start copying and sorting the partial results while the second wave of mappers is running. For all the experi- ments, we set the similarity threshold σ = 0.9. Figure 3.6 shows the running times of the four different algorithms. All of them have a quadratic step, so doubling the size of the input roughly multiplies by 4 the running time. Unexpectedly, VERN does not improve significantly over ELSA. This means that Prefix-Filtering is not fully exploited. Recall ELSA uses a simple Term-Filtering and compares any document pair sharing at least one term. Both our proposed algo- rithms outperform the two baselines. In particular, SSJ-2 is more than twice faster than VERN and SSJ-2R is about 4.5 times faster. Notice that 58
- 77. SSJ-2R is twice as fast compared to SSJ-2, which means that the im- provement given by the use of the remainder file is significant. We tried to fit a simple power law model f(x) = axb to the running time of the algorithms. For all algorithms but VERN the parameter b 2.5, while a 10−8 with ELSA having the largest one. VERN has a smaller constant a 10−10 with a larger b 2.9. However, given the small number of data points available the analysis is not conclusive. 3.6.2 Map phase 0 1000 2000 3000 4000 5000 6000 7000 8000 15000 20000 25000 30000 35000 40000 45000 50000 55000 60000 65000 Time(seconds) Number of vectors ELSA VERN SSJ-2 SSJ-2R Figure 3.7: Average mapper completion time. In Figure 3.7 we report the average map times for each algorithm. Clearly VERN is the fastest. The mapper only replicates input docu- ments. The time required by the other algorithms grows quadratically as expected. The two algorithms we propose are two times faster than ELSA for two main reasons. 59
- 78. 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 10 20 30 40 50 Time(seconds) Mapper ID ELSA VERN SSJ-2R without bucketing SSJ-2R with bucketing Figure 3.8: Mapper completion time distribution. First, Prefix-Filtering reduces the maximum inverted list length. Even a small improvement here brings a quadratic gain. Since Prefix-Filtering removes the most frequent terms, the longest inverted lists are short- ened or even removed. For D17K, the length of the longest inverted list is reduced from 6600 to 1729 thanks to Prefix-Filtering, as shown in Fig- ure 3.9. The time to process such inverted list decreases dramatically, and also the amount of intermediate data generated is reduced. Interestingly, Prefix-Filtering does not affect significantly the index size. Only 10% of the index is pruned as reported in Table 3.4, meaning that its effects are limited to shortening the longest inverted lists. Second, we employ a bucketing technique to improve load balancing. Since mappers process the inverted lists in chunks, the longest inverted lists might end up in the same chunk and be processed by a single map- per. SSJ-2 and SSJ-2R randomly hash the inverted lists into different 60
- 79. Table 3.4: Statistics for the four algorithms on the three datasets.Dataset Algorithm #evaluatedpairs(M) Indexsize(MB) Remaindersize(MB) Shufflesize(GB) Runningtime(s) Avg.maptime(s) Std.maptime(%) Avg.reducetime(s) Std.reducetime(%) D17K ELSA 109 46 3.3 2,187 276 127.50 49 16.68 VERN 401 3.7 1,543 42 68.10 892 22.20 SSJ-2 65 41 2.1 971 148 37.92 575 3.58 SSJ-2R 65 41 4.7 2.6 364 122 26.50 49 15.50 D30K ELSA 346 92 11.3 8,430 1,230 132.08 82 15.91 VERN 1,586 8.3 5,313 112 68.10 3,847 13.94 SSJ-2 224 82 8.1 3,862 635 32.06 2,183 5.81 SSJ-2R 224 82 8.2 10.5 1,571 560 23.41 155 15.50 D63K ELSA 1,519 189 49.2 51,540 7,013 136.39 1,136 11.84 VERN 6,871 20.7 28,534 338 59.61 16,849 9.36 SSJ-2 1,035 170 35.8 20,944 3,908 24.32 11,328 2.76 SSJ-2R 1,035 170 15.6 49.7 9,745 3,704 20.26 846 12.11 buckets, so that the longest lists are likely spread among all the map- pers. Figure 3.8 shows the completion time of the mappers for the D17K dataset. VERN has the lowest average mapper completion time, as all the work is done in the reducer. However, due to skew in the input, the slowest mapper in VERN is slower than in SSJ-2R with bucketing. This can happen if there are a few very dense documents in the input, so that VERN needs to create a large number of copies of each of these docu- ment. ELSA is in any case slower than SSJ-2R without bucketing just because of the maximum inverted list length. Nevertheless, completion times are not evenly distributed in ELSA. This skew induces a strong load imbalance, forcing all the reducers to wait the slowest mapper be- fore starting. Bucketing solves this issue by evenly spreading the load among mappers. As a result, the running time of the slowest mapper is almost halved. The standard deviation of map completion times for all algorithms is reported in Table 3.4. 61
- 80. 1 10 100 1000 100 1000 Numberoflists Inverted list length max=6600 ELSA 1 10 100 1000 Numberoflists max=1729 SSJ-2R Figure 3.9: Effect of Prefix-filtering on inverted list length distribution. 3.6.3 Shuffle size Figure 3.10 shows the shuffles sizes for the various algorithms when varying the input size. The shuffle size is affected by the combiners, that compact the key-value pairs emitted by the mappers into partial results by applying a reduce-like function. VERN has the smallest shuffle size. We intuitively expected that the replication performed during the map phase would generate a large amount of intermediate data. Conversely, the algorithms based on the inverted index generate the largest volume of data. This is consistent with the analysis in the previous section as VERN is the only algorithm without a quadratic term in the shuffle size. More specifically, SSJ-2 produces less data thanks to Prefix-Filtering. However, SSJ-2R shuffles about the same data as ELSA due to the addi- tional information needed the replication introduced by the partitioning of the remainder file. The shuffles size does not include the remainder 62
- 81. 0 5 10 15 20 25 30 35 40 45 50 15000 20000 25000 30000 35000 40000 45000 50000 55000 60000 65000 Shufflesize(GB) Number of vectors ELSA VERN SSJ-2 SSJ-2R Figure 3.10: Shuffle size. file, which is anyway small enough to be negligible as discussed below. Although SSJ-2R and ELSA have the same shuffle size, our algorithm is almost five times faster overall. 3.6.4 Reduce phase Figure 3.11 shows the average running time of the reduce function. VERN is the most expensive as expected. While the other algorithms take ad- vantage of the MR infrastructure to perform partial similarity computa- tions, VERN just delivers to the reducer a collection of potentially similar documents. The similarity computation is entirely done at the reducer, with a cost quadratic in the number of documents received. In addition, the same document pair is evaluated several times at different reducers at least to check if the reducer is responsible for computing the similarity, thus increasing the total cost of the reduce phase. 63
- 82. 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 15000 20000 25000 30000 35000 40000 45000 50000 55000 60000 65000 Time(seconds) Number of vectors ELSA VERN SSJ-2 SSJ-2R Figure 3.11: Average reducer completion time. SSJ-2 is the second most expensive due to the remote retrieval of doc- uments from the distributed file system. Both SSJ-2R and ELSA are way faster compared to the other two algo- rithms. The reducer performs very little computation, the contributions from the various terms are simply summed up. The use of the remainder file significantly speeds up SSJ-2R compared to SSJ-2. The remainder file is quickly retrieved from the distributed file system and no random remote access is performed. The performance of the reducer depends heavily on the number of candidate pairs evaluated. As shown in Table 3.4, both SSJ-2 and SSJ-2R evaluate about 33% less candidate than ELSA. VERN evaluates a number of pairs which is more than 5 times larger than SSJ-2 and SSJ-2R be- cause of the replication of the input sent to the reducers. Even though all but one of these pairs are discarded, they still need to be checked. 64
- 83. As reported in Table 3.4, all reduce times have small standard deviation, which means that the load is well balanced across the reducers. 3.6.5 Partitioning the remainder file 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 1 2 3 4 5 6 7 Size(kB) Number of partitions K Remainder file Ideal remainder file (1/x) Shuffle Figure 3.12: Remainder file and shuffle size varying K. We have seen that using the remainder file in SSJ-2R almost halves the running time of SSJ-2. This result leverages the fact that the portion of information which is needed by every node can be easily broadcast via the distributed file system rather than inside the MR data flow. In Table 3.4, we report the size of the remainder file which is always about 10% of the inverted index when using a similarity threshold σ = 0.9. Such limited size was not an issue in our experimental setting. How- ever, this might become an issue with larger collections, or when many reducers run on the same node and share the same memory. 65
- 84. Figure 3.12 illustrates a small experiment on a single node with the D17K dataset, where we varied the number K of chunks of the remainder file. Since partitioning is done in the document identifier space, the size of each chunk is not exactly the same and depends on the distribution of document sizes. However, in our experiments the variance is quite low. This proves experimentally that a reducer needs to load in memory only a small chunk, thus allowing SSJ-2R to scale to very large collections. Figure 3.12 also shows the trade-off between shuffle size and remainder file size when increasing K. For each additional chunk we need to shuffle one extra copy of the input, so shuffle size increases linearly with K. 3.7 Conclusions Finding similar items in a bag of documents is a challenging problem that arises in many applications in the areas of Web mining and information retrieval. The size of Web-related problems mandates the use of parallel approaches in order to achieve reasonable computing times. In this chapter we presented two novel algorithms for the MapRe- duce framework. We showed that designing efficient algorithms for MR is not trivial and requires careful blending of several factors to effectively capitalize on the available parallelism. We analyzed the complexity of our algorithms, and compared it with the state-of-the-art by examining the map, shuffle and reduce phases. We validated this theoretical analy- sis with experimental evidence collected on a sample of the Web. SSJ-2R borrows from previous approaches based on inverted index, and embeds pruning strategies that have been used only in sequential algorithms so far. We exploited the underlying distributed filesystem to support communication patterns that do not naturally fit the MR frame- work. We also described a partitioning strategy that overcomes memory limitations at the cost of an increased volume of intermediate data. SSJ- 2R achieves scalability without sacrificing precision by exploiting each MR phase to perform useful work. Thanks to a careful design that takes into account the specific properties of MR, SSJ-2R outperforms the state- of-the-art by a factor of about 4.5. 66
- 85. Chapter 4 Social Content Matching in MapReduce Matching is a classical problem in graph theory. It entails finding a sub- set of edges that satisfy a bound on the number of shared vertexes. This kind of problem falls in the second category of the taxonomy defined in Chapter 1 and requires iterative solutions. Matching problems are ubiq- uitous. They occur in economic markets and Web advertising, to name a few. In this chapter we focus on an application of matching for social media. Our goal is to distribute content from information suppliers to in- formation consumers. We seek to maximize the overall relevance of the matched content from suppliers to consumers while regulating the over- all activity, e.g., ensuring that no consumer is overwhelmed with data and that all suppliers have chances to deliver their content. We propose two MapReduce matching algorithms: GREEDYMR and STACKMR. Both algorithms have provable approximation guarantees, and in practice they produce high-quality solutions. While both algo- rithms scale extremely well, we can show that STACKMR requires only a poly-logarithmic number of MapReduce steps, making it an attrac- tive option for applications with very large datasets. We experimentally show the trade-offs between quality and efficiency of our solutions on two large datasets coming from real-world social media Web sites. 67
- 86. 4.1 Introduction The last decade has witnessed a radical paradigm shift on how informa- tion content is distributed among people. Traditionally, most of the in- formation content has been produced by few specialized agents and con- sumed by the big masses. Nowadays, an increasing number of platforms allow everyone to participate both in information production and in in- formation consumption. The phenomenon has been coined as democrati- zation of content. The Internet, and its younger children, user-generated content and social media, have had a major role in this paradigm shift. Blogs, micro-blogs, social-bookmarking sites, photo-sharing systems, and question-answering portals, are some of the social media that people participate in as both information suppliers and information consumers. In such social systems, not only consumers have many opportunities to find relevant content, but also suppliers have opportunities to find the right audience for their content and receive appropriate feedback. How- ever, as the opportunities to find relevant information and relevant au- dience increase, so does the complexity of a system that would allow suppliers and consumers to meet in the most efficient way. Our motivation is building a “featured item” component for social- media applications. Such a component would provide recommendations to consumers each time they log in the system. For example, flickr1 dis- plays photos to users when they enter their personal pages, while Yahoo! Answers2 displays questions that are still open for answering. For con- sumers it is desirable that the recommendations are of high quality and relevant to their interests. For suppliers it is desirable that their content is delivered to consumers who are interested in it and may provide useful feedback. In this way, both consumers and suppliers are more satisfied by using the system and they get the best out of it. Naturally, we model this problem as a matching problem. We asso- ciate a relevance score to each potential match of an item t to a user u. This score can be seen as the weight of the edge (t, u) of the bipartite 1http://flickr.com 2http://answers.yahoo.com 68
- 87. graph between items and users. For each item t and each user u we also consider constraints on the maximum number of edges that t and u can participate in the matching. These capacity constraints can be estimated by the activity of each user and the relative frequency with which items need to be delivered. The goal is to find a matching that satisfies all capacity constraints and maximizes the total weight of the edges in the matching. This problem is known as b-matching . The b-matching problem can be solved exactly in polynomial time by max-flow techniques. However, the fastest exact algorithms today have complexity ˜O(nm) (Gabow, 1983; Goldberg and Rao, 1998), for graphs with n nodes and m edges, and thus do not scale to large datasets. In- stead, in this work we focus on approximation algorithms that are scal- able to very large datasets. We propose two algorithms for b-matching, STACKMR and GREEDYMR, which can be implemented efficiently in the MapReduce paradigm. While both our algorithms have provable ap- proximation guarantees, they have different properties. We design the STACKMR algorithm by drawing inspiration from ex- isting distributed algorithms for matching problems (Garrido et al., 1996; Panconesi and Sozio, 2010). STACKMR is allowed to violate capacity con- straints by a factor of (1 + ), and yields an approximation guarantee of 1 6+ , for any > 0. We show that STACKMR requires a poly-logarithmic number of MapReduce steps. This makes STACKMR appropriate for re- alistic scenarios with large datasets. We also study a variant of STACK- MR, called STACKGREEDYMR, in which we incorporate a greedy heuris- tic in order to obtain higher-quality results. On the other hand, GREEDYMR is simpler to implement and has the desirable property that it can be stopped at any time and provide the current best solution. GREEDYMR is a 1/2-approximation algorithm, so it has a better quality guarantee than STACKMR. GREEDYMR also yields better solutions in practice. However, it cannot guarantee a poly- logarithmic number of steps. A simple example shows that GREEDYMR may require a linear number of steps. Although GREEDYMR is theo- retically less attractive than STACKMR, in practice it is a very efficient algorithm, and its performance is way far from the worst case. 69
- 88. Finally, we note that the b-matching algorithm takes as input the set of candidate edges weighted by their relevance scores. In some cases, this set of candidate edges is small, for instance when items are recom- mended only among friends in a social network. In other applications, any item can be delivered to any user, e.g., a user in flickr may view a photo of any other user. In the latter case, the graph is not explicit, and we need to operate on a bag of items and consumers. In this case, materi- alizing all pairs of item-user edges is an unfeasible task. Thus, we equip our framework with a scheme that finds all edges with score greater than some threshold σ, and we restrict the matching to those edges. We use the SSJ-2R algorithm presented in Chapter 3 to solve the problem of find- ing all similar item-user pairs efficiently in MapReduce. Our main contributions are the following. • We investigate the problem of b-matching in the context of social con- tent distribution, and devise a MapReduce framework to address it. • We develop STACKMR, an efficient variant of the algorithm presented by Panconesi and Sozio (2010). We demonstrate how to adapt such an algorithm in MapReduce, while requiring only a poly-logarithmic number of steps. Our experiments show that STACKMR scales excel- lently to very large datasets. • We introduce GREEDYMR, a MapReduce adaptation of a classical greedy algorithm. It has a 1/2-approximation guarantee, and is very efficient in practice. • We employ SSJ-2R to build the input graph for the b-matching. • We perform a thorough experimental evaluation using large datasets extracted from real-world scenarios. The rest of the chapter is organized as follows. In Section 4.3 we for- mally define the graph matching problem. In Section 4.4 we present the application scenario to social content distribution that we consider. In Section 4.5 we discuss the algorithms and their MR implementation. Fi- nally, we present our experimental evaluation in Section 4.6. 70
- 89. 4.2 Related work The general problem of assigning entities to users so to satisfy some con- straints on the overall assignment arises in many different research areas of computer science. Entities could be advertisements (Charles et al., 2010), items in an auction (Penn and Tennenholtz, 2000), scientific pa- pers (Garg et al., 2010) or media content, like in our case. The b-matching problem finds applications also in machine learning (Jebara et al., 2009) and in particular in spectral clustering (Jebara and Shchogolev, 2006). The weighted b-matching problem can be solved in polynomial time by employing maximum flow techniques (Gabow, 1983; Goldberg and Rao, 1998). In any case, the time complexity is still superlinear in the worst case. Christiano et al. (2010) have recently developed a faster ap- proximation algorithm based on electrical flows. In a distributed environment, there are some results for the unweighted version of the (simple) matching problem (Fischer et al., 1993; Garrido et al., 1996), while for the weighted case the approximation guarantee has progressively improved from 1/5 (Wattenhofer and Wattenhofer, 2004) to 1/2 (Lotker et al., 2008). For distributed weighted b-matching, a 1/2- approximation algorithm was developed by Koufogiannakis and Young (2009). However, a MapReduce implementation is non-obvious. Lattanzi et al. (2011) recently proposed a MapReduce algorithm for b-matching. 4.3 Problem definition In this section we introduce our notation and provide our problem for- mulation. We are given a set of content items T = {t1, . . . , tn}, which are to be delivered to a set of consumers C = {c1, . . . , cm}. For each ti and cj, we assume we are able to measure the interest of consumer cj in item ti with a positive weight w(ti, cj). The distribution of the items T to the consumers C can be clearly seen as a matching problem on the bipartite graph with nodes T and C, and edge weights w(ti, cj). In order to avoid that each consumer cj receive too many items, we enforce a capacity constraint b(cj) on the number of items that are matched 71
- 90. to cj. Similarly, we would like to avoid the scenario when only a few items (e.g. the most popular ones) participate in the matching. To this end, we introduce a capacity constraint b(ti) on the number of consumers that each item ti is matched to. This variant of the matching problem is well known in the theoretical computer science community as the b-matching problem. This is defined as follows. We are given an undirected graph G = (V, E), a function b : V → N expressing node capacities (or budgets) and another function w : E → R+ expressing edge weights. A b-matching in G is a subset of E such that for each node v ∈ V at most b(v) edges incident to v are in the matching. We wish to find a b-matching of maximum weight. Although our algorithms work with any undirected graph, we focus on bipartite graphs which are relevant to our application scenarios. The problem we shall consider in the rest of the chapter is defined as follows. Problem 2 (Social Content Matching Problem). We are given an undirected bipartite graph G = (T, C, E), where T represents a set of items and C repre- sents a set of consumers, a weight function w : E → R+ , as well as a capacity function b : T ∪ C → N. A b-matching in G is a subset of E such that for each node v ∈ T ∪ C at most b(v) edges incident to v are in the matching. We wish to find a b-matching of maximum weight. 4.4 Application scenarios To instantiate the problem we just defined, we need to (i) define the weights w(ti, cj) between items ti and consumers cj, (ii) decide the set of potential edges that participates in the matching, and (iii) define the capacity constraints b(ti) and b(cj). In our work we focus only on the matching algorithm and we assume that addressing the details of the above questions depends on the application. However, for completeness we discuss our thoughts on these issues. Scenario. We envision a scenario in which an application operates in consecutive phases. Depending on the dynamics of the application, the duration of each phase may range from hours to days. Before the be- ginning of the i-th phase the application makes a tentative allocation of 72
- 91. which items will be delivered to which consumers during the i-th phase. The items that participate in this allocation, i.e., the set T of Problem 2, are those that have been produced during the (i − 1)-th phase, and per- haps other items that have not been distributed in previous phases. Edge weights. A simple approach is to represent items and consumers in a vector space, i.e., items ti and consumers cj are represented by feature vectors v(ti) and v(cj). Then we can define the edge weight w(ti, cj) using the cosine similarity w(ti, cj) = v(ti) · v(cj)/( v(ti) · v(cj) ). Potentially, more complex similarity functions can be used. Borrowing ideas from information retrieval, the features in the vector representation can be weighted by tf·idf scores. Alternatively, the weights w(ti, cj) could be the output of a recommendation system that takes into account user preferences and user activities. Candidate edges. With respect to deciding which edges to consider for matching, the simplest approach is to consider all possible pairs (ti, cj). This is particularly attractive, since we let the decision of selecting edges entirely to the matching algorithm. However, considering O(|T||C|) edges makes the system highly inefficient. Thus, we opt for methods that prune the number of candidate edges. Our approach is to consider as candi- dates only edges whose weight w(ti, cj) is above a threshold σ. The ra- tionale is that since the matching algorithm will seek to maximize the total edge weight, we preferably discard low-weight edges. We note that depending on the application, there may be other ways to define the set of candidate edges. For example, in social-networking sites it is common for consumers to subscribe to suppliers they are inter- ested in. In such an application, we consider only candidate edges (ti, cj) for which cj has subscribed to the supplier of ti. Capacity constraints. The consumer capacity constraints express the number of items that need to be displayed to each consumer. For ex- ample, if we display one different item to a consumer each time they access the application, b(cj) can be set to an estimate of the number of times that consumer cj will access the application during the i-th phase. Such an estimate can be obtained from log data. For the item capacity constraints, we observe that B = c∈C b(c) is 73
- 92. an upper bound on the total number of distributed items, so we require B = t∈T b(t) as well. Now we distinguish two cases, depending on whether there is a quality assessment on the items T or not. If there is no quality assessment, all items are considered equivalent, and the total distribution bandwidth B can be divided equally among all items, so b(t) = max{1, B |T | }, for all t in T. If on the other hand there is a quality assessment on the items T, we assume a quality estimate q(t) for each item t. Such an estimate can be computed using a machine-learning approach, as the one proposed by Agichtein et al. (2008), which involves various features like content, links, and reputation. Without loss of generality we assume normalized scores, i.e., t∈T q(t) = 1. We can then divide the total distribution bandwidth B among all items in proportion to their quality score, so b(t) = max{1, q(t) · B}. In a real-application scenario, the designers of the application may want to control the function q(t) so that it satisfies certain properties, for instance, it follows a power-law distribution. 4.5 Algorithms 4.5.1 Computing the set of candidate edges The first step of our algorithm is to compute the set of candidate edges, which in Section 4.4 were defined to be the edges with weight w(ti, cj) above a threshold σ. This step is crucial in order to avoid considering O(|T||C|) edges, which would make the algorithm impractical. As we have already seen in the previous chapter, the problem of find- ing all the pairs of ti ∈ T and cj ∈ C so that w(ti, cj) ≥ σ is known as the similarity join problem. Since we aim at developing the complete system in the MapReduce framework, we obviously take advantage of SSJ-2R. In particular, we adapt SSJ-2R to compute the similarity between item-consumer pairs. First, we build a document bag by interpreting the items ti and the consumers cj as documents via their vector repre- sentation. Second, SSJ-2R can be trivially modified to join the two sets T and C without considering pairs between two items or two consumers. 74
- 93. 4.5.2 The STACKMR algorithm Our first matching algorithm, STACKMR, is a variant of the algorithm developed by Panconesi and Sozio (2010). Panconesi and Sozio propose a complex mechanism to ensure that capacity constraints are satisfied, which unfortunately does not seem to have an efficient implementation in MapReduce. Here we devise a more practical variant that allows node capacities to be violated by a factor of at most (1 + ), for any > 0. This approximation is a small price to pay in our application scenarios, where small capacity violations can be tolerated. For the sake of presentation, we describe our algorithm first in a cen- tralized environment and then in a parallel environment. Pseudocode for STACKMR and for the algorithm by Panconesi and Sozio are shown in Algorithms 1 and 2, respectively. The latter one has been slightly changed so to take into account im- plementation issues. However, we do not include an evaluation of the latter algorithm as it does not seem to be efficient. In the next section we describe in detail how to implement the former algorithm in MapReduce. Our algorithm is based on the primal-dual schema, a successful and established technique to develop approximation algorithms. The primal- dual schema has proved to play an important role in the design of se- quential and distributed approximation algorithms. We hold the belief that primal-dual algorithms bear the potential of playing an important role in the design of MapReduce algorithms as well. The first step of any primal-dual algorithm is to formulate the prob- lem at hand as an integer linear program (IP). Each element that might be included in a solution is associated with a 0-1 variable. The combina- torial structure of the problem is captured by an objective function and a set of constraints, both being a linear combination of the binary variables. Then, integrality constraints are relaxed so that variables can take any value in the range [0, 1]. This linear program is called primal. From the primal program we derive the so-called dual. There is a direct correspon- dence between the variables of the primal and the constraints of the dual, as well as, the variables of the dual and the constraints of the primal. 75
- 94. Algorithm 1 STACKMR violating capacity constraints by a factor of at most (1+ ) 1: /* Pushing Stage */ 2: while E is non empty do 3: Compute a maximal b -matching M (each vertex v has capacity b(v) ), using the procedure in Garrido et al. (1996); 4: Push all edges of M on the distributed stack (M becomes a layer of the stack); 5: for all e ∈ M in parallel do 6: Let δ(e) = (w(e) − yu/b(u) − yv/b(v)) /2; 7: increase yu and yv by δ(e); 8: end for 9: Update E by eliminating all edges that have become weakly cov- ered 10: end while 11: /* Popping Stage */ 12: while the distributed stack is nonempty do 13: Pop a layer M out of the distributed stack. 14: In parallel include all edges of M in the solution. 15: For each vertex v: let ¯b(v) be the set of edges in M that are incident to v; update b(v) ← b(v) − ¯b(v); if b(v) ≤ 0 then remove all edges incident to v. 16: end while A typical primal-dual algorithm proceeds as follows: at each step dual variables are raised and as soon as a dual constraint is satisfied with equality (or almost) the corresponding primal variable is set to one. The above procedure is iterated until no dual variable can be increased further without violating a dual constraint. The approximation guaran- tee follows from the fact that any feasible dual solution gives an upper bound on any optimum solution for the primal. Thus, the closer these two quantities the better the approximation guarantee. We first present our algorithm in a centralized environment and later proceed to show how to adapt it in MapReduce. Let us now give the IP formulation for the b-matching problem. 76
- 95. Algorithm 2 STACKMR satisfying all capacity constraints 1: /* Pushing Stage */ 2: while E is non empty do 3: Compute a maximal b -matching M (each vertex v has capacity b(v) ), using the procedure in Garrido et al. (1996); 4: Push all edges of M on the distributed stack (M becomes a layer of the stack); 5: for all e ∈ M in parallel do 6: Let δ(e) = (w(e) − yu/b(u) − yv/b(v)) /2; 7: increase yu and yv by δ(e); 8: end for 9: Update E by eliminating all edges that have become weakly covered 10: end while 11: /* Popping Stage */ 12: while the distributed stack is nonempty do 13: Pop a layer M out of the distributed stack. 14: In parallel tentatively include all edges of M in the solution. 15: If there is a vertex v whose capacity is exceeded then mark all edges in M incident to v as overflow, remove them from the solution and remove all edges in E M incident to v from the graph. 16: For each vertex v: let ¯b(v) be the number of edges in M that are incident to v; update b(v) ← b(v) − ¯b(v); if b(v) = 0 then remove all edges incident to v. 17: end while 18: /* Computing a feasible solution */ 19: while there are overflow edges do 20: Let ¯L be the set of overflow edges such that for every e ∈ ¯L there is no overflow edge f, incompatible with e, for which δ(f) > (1 + )δ(e). 21: Compute a maximal b-matching ¯M including only edges of ¯L ( ¯M shall be referred to as a sublayer of the stack); 22: In parallel, for each edge e ∈ ¯M, include e in the solution if this maintains the solution feasible. 23: For each vertex v: let ¯b(v) be the set of edges in ¯M that are incident to v (these edges are included in the solution); update b(v) ← b(v) − ¯b(v); if b(v) ≤ 0 then remove from the set of overflow edges all edges incident to v. 24: Remove all edges in ¯M from the set of overflow edges. 25: end while 77
- 96. maximize e∈E w(e)xe (IP) such that e∈E, v∈e xe ≤ b(v) ∀v ∈ V, (4.1) where xe ∈ {0, 1} is associated to edge e, and a value of 1 means that e belongs to the solution. The dual program is as follows. minimize v∈V yv (DP) such that yu b(u) + yv b(v) ≥ w(e) ∀e = (u, v) ∈ E, (4.2) yv ≥ 0 ∀v ∈ V. (4.3) Dual constraints (4.2) are associated with edges e. An edge is said to be covered if its corresponding constraint is satisfied with equality. The variables occurring in such a constraint are referred as e’s dual variables and play an important role in the execution of the algorithm. The centralized algorithm consists of two phases: a push phase where edges are pushed on a stack in arbitrary order, and a pop phase where edges are popped from the stack and a feasible solution is computed. When an edge e(u, v) is pushed on the stack, each of its dual variables is increased by the same amount δ(e) so to satisfy Equation (4.2) with equality. The amount δ(e) is derived from Equation (4.2) as δ(e) = (w(e) − yu/b(u) − yv/b(v)) 2 . (4.4) Whenever edges become covered they are deleted from the input graph. The push phase terminates when no edge is left. In the pop phase, edges are successively popped out of the stack and included in the solution if feasibility is maintained. In a parallel environment, we wish to parallelize as many operations as possible so to ensure poly-logarithmic running time. Thus, we need a mechanism to bound the number of push and pop steps, which in the 78
- 97. centralized algorithm may be linear in the number of edges. This is done by computing at each step a maximal b -matching. Note the difference between maximum and maximal: a b-matching is maximal if and only if it is not properly contained in any other b-matching. All edges in a maximal set, called a layer of the stack, are pushed on the stack in parallel. In the popping phase, all edges within the same layer are popped out of the stack and included in the solution in parallel. Edges of nodes whose capacity constraints are satisfied or violated are deleted from the stack and ignored from further consideration. A maximal b-matching can be computed efficiently in MapReduce as we will discuss in Section 4.5.3. Unfortunately, the total number of layers may still be linear in the maximum degree of a node. To circumvent this problem, we introduce the definition of weakly covered edges. Roughly speaking, a weakly cov- ered edge is an edge whose constraint is only “partially satisfied” and thus gets covered after a small number of iterations. Definition 1. (Weakly covered edges) Given > 0, at any time during the execution of our algorithm we say that an edge e ∈ E is weakly covered if constraint (4.2) for e = uv is such that ¯yu b(u) + ¯yv b(v) ≥ 1 3 + 2 w(e), (4.5) where ¯y denotes the current value of y. Observe that Equation (4.5) is derived from Equation (4.2). To summarize, our parallel algorithm proceeds as follows. At each step of the push phase, we compute a maximal b -matching using the procedure by Garrido et al.. All the edges in the maximal matching are then pushed on the stack in parallel forming a layer of the stack. For each of these edges we increase each of its dual variable by δ(e) in parallel. Some edges might then become weakly covered and are deleted from the input graph. The push phase is executed until no edge is left. At the end of the push phase, layers are iteratively popped out of the stack and edges within the same layer are included in the solution in parallel. This can violate node capacities by a factor of at most (1 + ), as every layer contains at most b(v) edges incident to any node v. Edges 79
- 98. Input Push Pop Output Figure 4.1: Example of a STACKMR run. of nodes whose capacity constraints are satisfied or violated are deleted from the stack and ignored from further consideration. This phase is iterated until the stack becomes empty. Figure 4.1 shows an example of a run of the STACKMR algorithm. On the top left we have the input: an undirected weighted graph. In the middle column the push phase builds the stack layer by layer, going upwards. Each layer is a maximal b -matching. On the right column the pop phase consumes the stack in reverse order and merges each layer to create the final solution. Edges in lower layers might get discarded if capacities are saturated. The output of the algorithm is shown on the bottom left, where dashed edges have been excluded by STACKMR. We can show that the approximation guarantee of our algorithm is 1 6+ , for every > 0. Moreover, we can show that the push phase is iter- ated at most O(log wmax wmin ) steps, where wmax and wmin are the maximum and minimum weight of any edge in input, respectively. This fact, to- gether with the fact that the procedure by Garrido et al. (1996) requires O(log3 n) rounds imply the following theorem. Theorem 1. Algorithm 1 has an approximation guarantee of 1 6+ and violates capacity constraints by a factor of at most 1 + . It requires O(log3 n 2 · log wmax wmin ) 80
- 99. communication rounds, with high probability. The non-determinism follows from the algorithm that computes max- imal b-matchings. The proof of Theorem 1 is similar to the one given by Panconesi and Sozio. STACKMR is a factor 1/ faster than the original. 4.5.3 Adaptation in MapReduce The distributed algorithm described in the previous section works in an iterative fashion. In each iteration we first compute a maximal matching, then we push it on a stack, we update edges, and we pop all levels from the stack. Below we describe how to implement these steps in MapReduce. Maximal matching. To find maximal b-matchings we employ the al- gorithm of Garrido et al. which is an iterative probabilistic algorithm. Each iteration consists of four stages: (i) marking, (ii) selection, (iii) matching, and (iv) cleanup. In the marking stage, each node v marks randomly 1 2 b(v) of its incident edges. In the selection stage, each node v selects randomly max{ 1 2 b(v) , 1} edges from those marked by its neighbors. Call F this set of selected edges. In the matching stage, if some node v has ca- pacity b(v) = 1 and two incident edges in F, it randomly deletes one of them. At this point the set F is a valid b-matching. The set F is added to the solution and removed from the original graph. In the cleanup stage, each node updates its capacity in order to take into consideration the edges in F and saturated nodes are removed from the graph. These stages are iterated until there are no more edges left in the original graph. The process requires, on expectation, O(log3 n) iterations to terminate. To adapt this algorithm in MapReduce, we need one job for each stage of the algorithm. The input and output of each MapReduce job is al- ways of the same format: a consistent view of the graph represented as adjacency lists. We maintain a node-based representation of the graph because we need to make decisions based on the local neighborhood of each node. Assuming the set of nodes adjacent to vi is {vj, . . . , vk}, the input and output of each job is a list of pairs vi, [(vj, Tij), . . . , (vk, Tik)] , where vi is the key and [(vj, Tj), . . . , (vk, Tk)] the associated value. The 81
- 100. variables T represent the state of each edge. We consider five possible states of an edge: E in the main graph; K marked; F selected; D deleted; and M in the matching. The 4 stages of the algorithm are repeated until all the edges are in the matching (M) or are deleted (D). The general signature of each job is as follows. Map: vi, [(vj, Tij), . . . , (vk, Tik)] → vi, T (i) ij , vj, T (i) ij , . . . , vi, T (i) ik , vk, T (i) ik Reduce: vi, T (i) ij , vi, T (j) ij , . . . , vi, T (i) ik , vk, T (k) ik → vi, [(vj, Tij), . . . , (vk, Tik)] where T (i) ij is the state of edge (vi, vj) as locally viewed by vi and Tij is the final state after unification of the views from vi and vj. Each Map function alters the state of the graph locally to each node. Each Reduce function unifies the diverging views of the graph at each node. For each edge (vi, vj), each Map function will emit both vi and vj as keys, together with the current state of the edge as value. The Reduce function will receive the views of the state of the edge from both end- points, and will unify them, yielding a consistent graph representation. Unification is performed by a simple precedence rule. If a b the algo- rithm unifies two diverging states (a, b) to state b. Only a subset of all the possible combinations of states may actually happen, so we need to specify only a few rules as follows. E K F; F M; E D; Each MapReduce job uses the same communication pattern and state unification rules. They only differ in the way they update the state of the edges. The communication cost of each job is thus O(|E|), while the achievable degree of parallelism is O(|V |). Figure 4.2 illustrates the com- munication pattern, which is the same for each vertex. Let us take into account the central node. For each incident edge, the mapper emits the edge state as viewed by the node twice: once for each end of the edge. In the picture the state view is represented by the arrows which are color coded to represent their origin and point to their destination. For each 82
- 101. Map Reduce Figure 4.2: Communication pattern for iterative graph algorithms on MR. incident edge, the reducer receives two different views of the state of the edge, one from each endpoint. The reducer reconciles the two views by applying the unification rules to obtain a consistent view of the graph. Push, update, and pop. The basic scheme of communication for the push, update, and pop phases is the same as the one for computing maximal matching. We maintain the same invariant of representing the graph from Map to Reduce functions and in-between consecutive iterations. For these phases of the algorithm, we maintain a separate state for each edge. The possible states in which an edge can be are: E, edge in the graph; S, edge stacked; R, edge removed from the graph; and I, edge included in the solution. For each edge we also maintain an integer vari- able that represents the stack level in which the edge has been put. During the push phase, for each edge included in the maximal match- ing, we set its state to S and the corresponding stack level. The update phase is needed to propagate the δ(e) contributions. Each edge sent to a node v carries the value of its sending node yu/b(u). Thus, each node can compute the new δ(e) and update its local yv. This phase also removes 83
- 102. weakly covered edges by setting their state to R, and updates the capac- ities of the nodes for the next maximal-matching phase. Removed edges are not considered for the next maximal-matching phase. The pop phase starts when all the edges in the graph are either stacked (S) or removed (R). During the pop phase, each stacked (S) edge in the current level (starting from the topmost) is included in the solution by setting its state to I. The capacities are locally updated, and nodes (and all incident edges) are removed when their capacity becomes non- positive. Overall, there is one MapReduce step for each stack level. The decision to change the state of the edge during these phases de- pends only on the current state of the edge. The only local decision is edge removal when the vertex capacity gets saturated. Therefore, we only need to deal with diverging views related to the removed (R) state: E R; S R; I R; 4.5.4 The GREEDYMR algorithm In this section we present a second matching algorithm based on a greedy strategy: GREEDYMR. As previously, we analyze the centralized version and then we show how to adapt it in MapReduce. The centralized greedy algorithm processes sequentially each edge in order of decreasing weight. It includes an edge e(u, v) in the solution if b(u) > 0 ∧ b(v) > 0. In this case, it subtracts 1 from both b(u) and b(v). It is immediate that the greedy algorithm produces a feasible solution. In addition, it has a factor 1/2 approximation guarantee. We believe that this is a well-known result, however, we were not able find a reference. Thus, for completeness we include a proof in Section 4.5.5. GREEDYMR is a MapReduce adaptation of this centralized algorithm. We note that the adaptation is not straightforward due to the access to the globally-shared variables b(v) that hold node capacities. GREEDYMR works as follows. In the map phase each node v proposes its b(v) edges with maximum weight to its neighbors. In the reduce phase, each node computes the intersection between its own proposals and the proposals of its neighbors. The set of edges in the intersection is 84
- 103. included in the solution. Then, each node updates its capacity. If it be- comes 0, the node is removed from the graph. Pseudocode for GREEDY- MR is shown in Algorithm 3. In contrast with STACKMR, GREEDYMR is not guaranteed to ter- minate in a poly-logarithmic number of iterations. As a simple worst- case input instance, consider a path graph u1u2, u2u3, ...uk−1uk such that w(ui, ui+1) ≤ w(ui+1, ui+2). GREEDYMR will face a chain of cascading updates that will cause a linear number of MapReduce iterations. How- ever, as shown in Section 4.6, in practice GREEDYMR yields quite com- petitive results compared to STACKMR. Finally, GREEDYMR maintains a feasible solution at each step. The advantage is that it can be terminated at any time and return the cur- rent solution. This property makes GREEDYMR especially attractive in our application scenarios, where content can be delivered to the users immediately while the algorithm continues running in the background. Algorithm 3 GREEDYMR 1: while E is non empty do 2: for all v ∈ V in parallel do 3: Let Lv be the set of b(v) edges incident to v with maximum weight; 4: Let F be Lv ∩LU where U = {u ∈ V : ∃ e(v, u) ∈ E} is the set f vertexes sharing an edge with v; 5: Update M ← M ∪ F; 6: Update E ← E F; 7: Update b(v) ← b(v) − bF (v); 8: If b(v) = 0 remove v from V and remove all edges incident to v from E; 9: end for 10: end while 11: return M; 4.5.5 Analysis of the GREEDYMR algorithm The following theorem proves the approximation guarantee of GREEDY- MR. We believe this result to be well-known, however we could not find a reference. Thus, we give a proof for completeness and self contain- ment. The greedy algorithm can be equivalently described as the follow- 85
- 104. ing process: at each step each node v marks an edge with largest weight. If an edge is marked by both its end nodes then it enters the solution and residual node capacities are updated. As soon as the residual capacity of a node becomes zero all its edges are deleted and ignored from further consideration. These steps are iterated until the set of edges of the input graph becomes empty. Theorem 2. The greedy algorithm produces a solution with approximation guarantee 1 2 for the weighted b-matching problem. Proof. Let O be an optimum solution for a given problem instance and let A be the solution yielded by the greedy algorithm. For every node v, let Ov and Av denote the sets of edges O∩∆G(v) and A∩∆G(v), respectively, where ∆G(v) is the set of edges in G incident to v. The total weight of a set of edges T is denoted by w(T). We say that a node is saturated if exactly b(v) edges of v are in the greedy solution A and we let S denote the set of saturated nodes. For every node v, we consider the sets Ov ⊆ Ov A, defined as fol- lows: each edge e(u, v) ∈ O A is assigned to a set Ov, for which v is a saturated node and the weight of any edge in Av is larger than w(e). Ties are broken arbitrarily. There must be such a node v, for otherwise e would be included in A. The idea of the proof is to relate the weight of edge e with the weights of the edges of Av, which prevent e from entering the solution. From the definition of the Ov’s it follows that w(O A) = v∈S w(Ov). (4.6) For every saturated node v we have that |Ov| ≤ b(v) = |Av|. From this and from the definition of the Ov’s we have that v∈S w(Av O) ≥ v∈S w(Ov). (4.7) From Equations (4.6) and (4.7) we obtain 2w(A) ≥ w(A ∩ O) + v∈S w(Av O) ≥ w(A ∩ O) + v∈S w(Ov) ≥ w(O), which concludes the proof. 86
- 105. The analysis is tight as proved by the following example. Consider a cycle consisting of three nodes u, v, z and three edges uv, vz, zu. Let b(u) = b(z) = 1 and let b(v) = 2. Moreover, let w(uv) = w(vz) = 1 while w(zu) = (1+ ) where > 0. The greedy algorithm would select the edge whose weight is 1 + , while the weight of the optimum solution is 2. 4.6 Experimental evaluation Flickr. We extract two datasets from flickr, a photo-sharing Web site. Table 4.1 shows statistics for the flickr-small and flickr-large datasets. In these datasets items represent photos and consumers repre- sent users. In each dataset, each user has posted at least 10 photos, and each photo has been considered at least 5 times as a favorite. Recall from our discussion in Section 4.4 that the capacity b(u) of each user u should be set in proportion to the login activity of the user in the system. Unfortunately, the login activity is not available in the datasets. So we decide to use the number of photos n(u) that the user u has posted as a proxy to his activity. We then use a parameter α > 0 to set the ca- pacity of each user u as b(u) = α n(u). Higher values of the parameter α simulate higher levels of activity in the system. Next we need to specify the capacity of photos. Since our primary goal is to study the matching algorithm, specifying the actual capacities is beyond the scope of the work. Thus we use as a proxy, the number of favorites f(p) that each photo p has received. The intuition is that we want to favor good photos in order to increase user satisfaction. Follow- ing Section 4.4, we set the capacity of each photo to b(p) = f(p) u αn(u) q f(q) . In order to estimate edge similarities, we represent each photo by its tags, and each user by the set of all tags he or she has used. Then we compute the similarity between a photo and a user as the cosine simi- larity of the their tag vectors. We compute all edges whose similarity is larger than a threshold σ by employing SSJ-2R. 87
- 106. 0 0.2 0.4 0.6 0.8 10 0 10 2 10 4 10 6 σ flickr small 0 0.2 0.4 0.6 0.8 1 10 4 10 6 10 8 10 10 σ flickr large 0 0.2 0.4 0.6 0.8 1 10 0 10 5 10 10 σ yahoo answers Figure 4.3: Distribution of edge similarities for the datasets. 88
- 107. 10 0 10 5 10 0 10 1 10 2 10 3 capacity flickr small 10 0 10 5 10 10 10 0 10 1 10 2 10 3 10 4 capacity flickr large 10 0 10 2 10 4 10 0 10 2 10 4 10 6 10 8 capacity yahoo answers Figure 4.4: Distribution of capacities for the three datasets. 89
- 108. Yahoo! Answers. We extract one dataset from Yahoo! Answers, a Web question-answering portal. In yahoo-answers, consumers represent users, while items represent questions. The motivating application is to propose unanswered questions to users. Matched questions should fit the interests of the user. To identify user interests, we represent users by the weighted set of words in their answers. We preprocess the answers to remove punctuation and stop-words, stem words, and apply tf·idf weighting. We treat questions in the same manner. As before, we extract a bipartite graph with edge weights represent- ing the similarity between questions and users. We employ again a thresh- old σ to sparsify the graph, and present results for different density lev- els. In this case, we set user capacities b(u) by employing the number of answers n(u) provided by each user u as a proxy to the activity of the user. We use the same parameter α as for the flickr datasets to set b(u) = α n(u). However, for this dataset we use a constant capacity for all questions, in order to test our algorithm under different settings. For each question q we set b(q) = u αn(u) |Q| . The distributions of node capacities are shown in Figure 4.4 while the distributions of edge similarities are shown in Figure 4.3. Variants. We also experiment with a number of variants of the STACKMR algorithm. In particular, we vary the edge-selection strategy employed in the first phase of the maximal b-matching algorithm (marking). The STACKMR algorithm proposes to its neighbors edges chosen uniformly at random. In order to favor heavier edges in the matching, we mod- ify the selection strategy to propose the 1 2 b(v) edges with the largest weight. We call this variant STACKGREEDYMR. We also experiment with a third variant, in which we choose edges randomly but with probability proportional to their weights. We choose not to show the results for this third variant because it always performs worse than STACKGREEDYMR Measures. We evaluate the proposed algorithms in terms of both quality and efficiency. Quality is measured in terms of b-matching value achieved, and efficiency in terms of the number of MapReduce iterations required. 90
- 109. Table 4.1: Dataset characteristics. |T|: number of items; |C|: number of users; |E|: total number of item-user pairs with non zero similarity. Dataset |T| |C| |E| flickr-small 2 817 526 550 667 flickr-large 373 373 32 707 1 995 123 827 yahoo-answers 4 852 689 1 149 714 18 847 281 236 We evaluate our algorithms by varying the following parameters: the similarity threshold σ, which controls the number of edges that partic- ipate in the matching; the factor α in determining capacities; and the slackness parameter used by STACKMR. Results. Sample results on the quality and efficiency of our matching algorithms for the three datasets, flickr-small, flickr-large, and yahoo-answers, are shown in Figures 4.5, 4.6, and 4.7, respectively. For each plot in these figures, we fix the parameters and α and we vary the similarity threshold σ. Our observations are summarized as follows. Quality. GREEDYMR consistently produces matchings with higher value than the two stack-based algorithms. Since GREEDYMR has bet- ter approximation guarantee, this result is in accordance with theory. In fact, GREEDYMR achieves better results even though the stack algo- rithms have the advantage of being allowed to exceed node capacities. However, as we will see next, the violations of the stack-based algo- rithms are very small, ranging from practically 0 to at most 6%. In the flickr-large dataset, GREEDYMR produces solutions that have on average 31% higher value than the solutions produced by STACKMR. In flickr-small and yahoo-answers, the improvement of GREEDYMR is 11% and 14%, respectively. When comparing the two stack algorithms, we see that STACKGREEDYMR is slightly better than STACKMR. Again the difference is more pronounced on the flickr-large dataset. We also observe that in general the b-matching value increases with the number edges. This behavior is expected, as the number of edges in- crease the algorithms have more flexibility. Since we add edges by lower- ing the edge weight threshold, the gain in the b-matching value tends to saturate. The only exception to this rule is for STACKGREEDYMR on the 91
- 110. 0 5 10 15 x 10 4 0 500 1000 1500 2000 Number of edges matchingvalue flickr small, a=0.2, e=1.0 GreedyMR StackMR StackGreedyMR 0 5 10 15 x 10 4 −10 0 10 20 30 40 50 Number of edges map−reduceiterations flickr small, a=0.2, e=1.0 GreedyMR StackMR StackGreedyMR 0 5 10 15 x 10 4 0 1000 2000 3000 Number of edges matchingvalue flickr small, a=0.8, e=1.0 GreedyMR StackMR StackGreedyMR 0 5 10 15 x 10 4 0 10 20 30 40 Number of edges map−reduceiterations flickr small, a=0.8, e=1.0 GreedyMR StackMR StackGreedyMR 0 5 10 15 x 10 4 0 1000 2000 3000 4000 5000 Number of edges matchingvalue flickr small, a=3.2, e=1.0 GreedyMR StackMR StackGreedyMR 0 5 10 15 x 10 4 −10 0 10 20 30 Number of edges map−reduceiterations flickr small, a=3.2, e=1.0 GreedyMR StackMR StackGreedyMR Figure 4.5: flickr-small dataset: matching value and number of itera- tions as a function of the number of edges. 92
- 111. 0 5 10 x 10 8 3.5 4 4.5 5 5.5 x 10 6 Number of edges matchingvalue flickr large, a=0.4, e=1.0 GreedyMR StackMR StackGreedyMR 0 5 10 x 10 8 50 100 150 200 250 300 Number of edges map−reduceiterations flickr large, a=0.4, e=1.0 GreedyMR StackMR StackGreedyMR 0 5 10 x 10 8 0.8 0.9 1 1.1 1.2 1.3 1.4 x 10 7 Number of edges matchingvalue flickr large, a=1.6, e=1.0 GreedyMR StackMR StackGreedyMR 0 5 10 x 10 8 50 100 150 200 250 300 350 Number of edges map−reduceiterations flickr large, a=1.6, e=1.0 GreedyMR StackMR StackGreedyMR 0 5 10 x 10 8 1.5 2 2.5 x 10 7 Number of edges matchingvalue flickr large, a=6.4, e=1.0 GreedyMR StackMR StackGreedyMR 0 5 10 x 10 8 50 100 150 200 250 300 350 Number of edges map−reduceiterations flickr large, a=6.4, e=1.0 GreedyMR StackMR StackGreedyMR Figure 4.6: flickr-large dataset: matching value and number of itera- tions as a function of the number of edges. 93
- 112. 0 1 2 3 4 x 10 8 1 1.5 2 2.5 3 3.5 x 10 5 Number of edges matchingvalue yahoo answers, a=0.4, e=1.0 GreedyMR StackMR StackGreedyMR 0 1 2 3 4 x 10 8 0 200 400 600 Number of edges map−reduceiterations yahoo answers, a=0.4, e=1.0 GreedyMR StackMR StackGreedyMR 0 1 2 3 4 x 10 8 2 4 6 8 10 x 10 5 Number of edges matchingvalue yahoo answers, a=1.6, e=1.0 GreedyMR StackMR StackGreedyMR 0 1 2 3 4 x 10 8 0 100 200 300 400 500 600 Number of edges map−reduceiterations yahoo answers, a=1.6, e=1.0 GreedyMR StackMR StackGreedyMR 0 1 2 3 4 x 10 8 0 0.5 1 1.5 2 2.5 3 x 10 6 Number of edges matchingvalue yahoo answers, a=6.4, e=1.0 GreedyMR StackMR StackGreedyMR 0 1 2 3 4 x 10 8 0 100 200 300 400 500 Number of edges map−reduceiterations yahoo answers, a=6.4, e=1.0 GreedyMR StackMR StackGreedyMR Figure 4.7: yahoo-answers dataset: matching value and number of itera- tions as a function of the number of edges. 94
- 113. 0 2 4 6 0 0.01 0.02 0.03 0.04 0.05 0.06 α effectiveviolation flickr large σ = 0.02 σ = 0.04 σ = 0.08 σ = 0.16 0 2 4 6 0 2 4 6 8 10 12 x 10 −5 α effectiveviolation yahoo answers σ = 0.08 σ = 0.16 σ = 0.32 Figure 4.8: Violation of capacities for STACKMR. flickr-large dataset. We believe this is due to the uneven capacity distribution for the flickr-large dataset, see Figure 4.4. Our belief is supported by fact that the decrease is less visible for higher values of α. Efficiency. Our findings validate the theory also in terms of efficiency. In most settings the stack algorithms perform better than GREEDYMR. The only exception is the flickr-small dataset. This dataset is very small, so the stack algorithms incur excessive overhead in computing maximal matchings. However, the power of the stack algorithms is best proven on the larger datasets. Not only they need less MapReduce steps than GREEDYMR, but they also scale extremely well. The performance of STACKMR is almost unaffected by increasing the number of edges. Capacity violations. As explained in Section 4.5.2, the two stack-based algorithms can exceed the capacity of the nodes by a factor of (1 + ). However, in our experiments the algorithms exhibit much lower viola- tions than the worst case. We compute the average violation as follows. = 1 |V | v∈V max{|M(v)| − b(v), 0} b(v) , where |M(v)| is the degree of node v in the matching M, and b(v) is the capacity for each node v in V . Figure 4.8 shows capacity violations for STACKMR. The violations for STACKGREEDYMR are similar. When 95
- 114. 0 50 100 150 200 250 0.4 0.6 0.8 1 number of iterations fractionofmatchingvalue flickr large σ = 0.08 α = 0.4 σ = 0.08 α = 1.6 σ = 0.16 α = 0.4 σ = 0.16 α = 1.6 0 200 400 600 0 0.2 0.4 0.6 0.8 1 number of iterations fractionofmatchingvalue yahoo answers σ = 0.08 α = 0.4 σ = 0.08 α = 1.6 σ = 0.16 α = 0.4 σ = 0.16 α = 1.6 Figure 4.9: Normalized value of the b-matching achieved by the GREEDY- MR algorithm as a function of the number of MapReduce iterations. = 1, for the flickr-large dataset the violation is as low as 6% in the worst case. As expected, more violations occur when more edges are allowed to participate in the matching, either by increasing the number of edges (by lowering σ) or the capacities of the nodes (by increasing α). On the other hand, for the yahoo-answers datasets, using the same = 1, the violations are practically zero for any combination of the other parameters. One reason for the difference between the violations in these two datasets may be the capacity distributions, as shown in Figure 4.4. For all practical purposes in our scenarios, these violations are negligible. Any-time stopping. An interesting property of GREEDYMR is that it produces a feasible but suboptimal solution at each iteration. This allows to stop the algorithm at any time, or to query the current solution and let the algorithm continue in the background. Furthermore, GREEDY- MR converges very fast to a good global solution. Figure 4.9 shows the value of the solution found by GREEDYMR as a function of the it- eration. For the three datasets, flickr-small, flickr-large, and yahoo-answers, the GREEDYMR algorithm reaches 95% of its final b- matching value within 28.91%, 44.18%, and 29.35% of the total number of iterations required, respectively. The latter three numbers are averages over all the parameter settings we tried in each dataset. 96
- 115. 4.7 Conclusions Graph problems arise continuously in the context of Web mining. In this chapter we investigate the graph b-matching problem and its application to content distribution. Our goal is to help users effectively experience Web 2.0 sites with large collections of user-generated content. We described two iterative MapReduce algorithms, STACKMR and GREEDYMR. Both algorithms rely on the same base communication pat- tern. This pattern is able to support a variety of computations and pro- vides a scalable building block for graph mining in MR. To the best of our knowledge, STACKMR and GREEDYMR are the first solutions to graph b-matching in MR. Both algorithms have prov- able approximation guarantees and scale to realistic-sized datasets. In addition STACKMR provably requires only a poly-logarithmic number of MapReduce iterations. On the other hand GREEDYMR has a better approximation guarantee and allows to query the solution at any time. We evaluated our algorithms on two large real-world datasets from the Web and highlighted the tradeoffs between quality and performance between the two solutions. GREEDYMR is a good solution for practi- tioners. In our experiments it consistently found the best b-matching value. Moreover, it is easy to implement and reason about. Neverthe- less, STACKMR has high theoretical and practical interest because of its better running time. It scales gracefully to massive datasets and offers high-quality results. 97
- 116. Chapter 5 Harnessing the Real-Time Web for Personalized News Recommendation Real-time Web is an umbrella term that encompasses several social micro- blogging services. It can be modeled as a graph of nodes exchanging streams of updates via publish-subscribe channels. As such it crosses the boundaries between graphs and streams as defined in the taxonomy of Chapter 1. Famous examples include Facebook’s news feed and Twitter. In this chapter we tackle the problem of mining the real-time Web to suggest articles from the news stream. We propose T.REX, a new methodology for generating personalized recommendations of news ar- ticles by leveraging the information in users’ Twitter persona. We use a mix of signals to model relevance of news articles for users: the content of the tweet stream of the users, the profile of their social circles, and recent topic popularity in news and Twitter streams. We validate our approach on a real-world dataset from Yahoo! news and one month of tweets that we use to build user profiles. We model the task as click prediction and learn a personalized ranking function from click-through data. Our results show that a mix of various signals from the real-time Web is an effective indicator of user interest in news. 98
- 117. 5.1 Introduction Information overload is a term referring to the difficulty in taking decisions or understanding an issue when there is more information than one can handle. Information overload is not a new problem. The term itself pre- cedes the Internet by several years Toffler (1984). However, digital and automated information processing has aggravated the problem to un- precedented levels, transforming it into one of the crucial issues in the modern information society. In this work we focus on one of the most common daily activities: reading news articles online. Every day the press produces thousands of news articles covering a wide spectrum of topics. For a user, finding relevant and interesting information in this ocean of news is a daunting task and a perfect example of information overload. News portals like Yahoo! news and Google news often resort to rec- ommender systems to help the user find relevant pieces of information. In recent years the most successful recommendation paradigm has been collaborative filtering (Adomavicius and Tuzhilin, 2005). Collaborative fil- tering requires the users to rate the items they like. The rating can be explicit (e.g., ‘like’, ‘+1’, number of stars) or implicit (e.g., click on a link, download). In both cases, collaborative filtering leverages a closed feed- back loop: user preferences are inferred by looking only at the user inter- action with the system itself. This approach suffers from a data sparsity problem, namely it is hard to make recommendations for users for whom there is little available information or for brand new items, since little or no feedback is available for such “cold” items. At the same time, at an increasingly rate, web users access news ar- ticles via micro-blogging services and the so-called real-time web. By subscribing to feeds of other users, such as friends, colleagues, domain experts and enthusiasts, as well as to organizations of interest, they ob- tain timely access to relevant and personalized information. Yet, infor- mation obtained by micro-blogging services is not complete as highly- relevant events could easily be missed by users if none of their contacts posts about these events. 99
- 118. We propose to recommend news articles to users by combining two sources of information, news streams and micro-blogs, and leveraging the best features of each. News streams have high coverage as they ag- gregate a very large volume of news articles obtained from many differ- ent news agencies. On the other hand, information obtained by micro- blogging services can be exploited to address the problems of information filtering and personalization, as users can be placed in the context of their social circles and personal interests. Our approach has the following advantages. First, we are able to leverage the information from social circles in order to offer personal- ized recommendations and overcome the data-sparsity problem. If we do not have enough information for a user, there should be significantly more information from the social circle of the user, which is presumably relevant. Second, more than once it has been reported that news break out earlier on the real-time web than in traditional media, and we would like to harness this property to provide timely recommendations. With more than 200 million users, Twitter is currently the most pop- ular real-time web service. Twitter is an emerging agora where users publish short text messages, also known as tweets, and organize them- selves into social networks. Interestingly, in many cases, news have been published and commented on Twitter before any other news agency, as in the case of Osama Bin-Laden’s death in 2011,1 or Tiger Wood’s car crash in 2009.2 Due to its popularity, traditional news providers, such as magazines, news agencies, have become Twitter users: they exploit Twitter and its social network to disseminate their contents. Example. In Figure 5.1 we show the normalized number of tweets and news articles regarding “Osama Bin Laden” during the time period be- tween May 1st and 4th, 2011. For the news, we also report the num- ber of clicks in the same period. We notice that the number of relevant tweets ramps up earlier than news, meaning that the information spread through Twitter even before any press release. Later on, while the num- ber of tweets decreases quickly, and stabilizes around a relatively small 1http://www.bbc.co.uk/news/technology-13257940 2http://techcrunch.com/2009/11/27/internet-twitter-tiger-woods 100
- 119. number of tweets, the number of published news continues to be quite large. The number of clicks on news articles follows somewhat the num- ber of published news, even though there is a significant delay until the time the users actually click and read an article on the topic. Figure 5.2 presents similar information for the “Joplin tornado.” In this case, even though there is a great activity both on Twitter and on news streams, users start reading the news only after one day. About 60% of the clicks on the news occur starting from 10 hours after its publication. -0.2 0 0.2 0.4 0.6 0.8 1 1.2 M ay-01 h20M ay-02 h00M ay-02 h04M ay-02 h08M ay-02 h12M ay-02 h16M ay-02 h20M ay-03 h00M ay-03 h04M ay-03 h08 news twitter clicks Figure 5.1: Osama Bin Laden trends on Twitter and news streams. The goal of this work is to reduce the delay between the publication of a news and its access by a user. We aim at helping the users in finding relevant news as soon as they are published. Our envisioned application scenario is a feature operating on a news aggregator like Yahoo! news or Google news. Our objective is to develop a recommendation system that provides the users with fresh, relevant news by leveraging their tweet 101
- 120. -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 M ay-22 h00M ay-22 h12M ay-23 h00M ay-23 h12M ay-24 h00M ay-24 h12M ay-25 h00M ay-25 h12M ay-26 h00 news twitter clicks Figure 5.2: Joplin tornado trends on Twitter and news streams. stream. Ideally, the users log into the news portal and link their Twitter account to their portal account in order to provide access to their tweet stream. The portal analyzes the tweet stream of the users and provides them personalized recommendations. Solving this problem poses a number of research challenges. First, the volume of tweets and news is significantly large. It is necessary to design a scalable recommender system able to handle millions of users, tweets and news. Second, both tweets and news are unbounded streams of items arriving in real-time. The set of news from which to choose recommendations is highly dynamic. In fact, news are published contin- uously and, more importantly, they are related to events that cannot be predicted in advance. Also, by nature, news have a short life cycle, since they are replaced by updated news on the same topic, or because they be- come obsolete. Therefore, a recommender system should be able to find 102
- 121. relevant news early, before they lose their value over time. Third, the nature of tweets, short and jargon-like, complicates the task of modeling the interests of users. Finally, personalization should leverage user profiles to drive the user to less popular news. But it should not prevent from suggesting news of general interest, even when unrelated to the user profile, e.g., the Fukushima accident. In summary, our contributions are the following. • We propose an adaptive, online recommendation system. In con- trast, typical recommendation systems operate in offline mode. • We present a new application of usage of tweets. Twitter has mainly been used to identify trending topics and analyzing information spread. Its application to recommendation has received little inter- est in the community. Our main recommendation system is called T.REX, for twitter-based news recommendation system. • Our system provides personalized recommendations by leverag- ing information from the tweet stream of users, as well as from the streams of their social circle. By incorporating social informa- tion we address the issue of data sparsity. When we do not have enough information for a user, for example for a new user or if a user rarely tweets, the available information in the social circle of the user provides a proxy to his interests. The rest of this chapter is organized as follows. In Section 5.3 we for- malize the news recommendation problem, and introduce our proposed personalized news ranking function. In Section 5.5 we describe the learn- ing process of the ranking function based on click data. In Section 5.6 we present the experimental setting used in the evaluation of our algorithms and our results. Finally, in Section 5.2 we discuss other related work. 103
- 122. 5.2 Related work Recommender systems can be roughly divided in two large categories: content-based and collaborative filtering (Goldberg et al., 1992). The large-scale system for generating personalized news recommen- dations proposed by Das et al. (2007) falls in the second category. The au- thors exploit a linear combination of three different content agnostic ap- proaches based only on click-through data: clustering of users based on minhashing, probabilistic latent semantic indexing of user profiles and news, and news co-visitation count. Even tough the system can update its recommendation immediately after a new click is observed, we have seen that click information arrives with a significant delay, and therefore it may fail in detecting emerging topics early. Using Twitter to provide fresh recommendations about emerging top- ics has received a large deal of attention recently. A number of stud- ies attempts to understand the Twitter social network, the information- spreading process, and to discover emerging topics of interesest over such a network (Bakshy et al., 2011; Cataldi et al., 2010; Java et al., 2007). Chen et al. (2010) propose a URL-recommender system from URLs posted in Twitter. A user study shows that both the user content-based profile, and the user social neighborhood plays a role, but, the most im- portant factor in the recommendation performance is given by the social ranking, i.e., the number of times a URL is mentioned among the neigh- borhood of a given user. The work presented by Garcia Esparza et al. (2010) exploits data from a micro-blogging movie review service similar to Twitter. The user profile is built on the basis of the user’s posts. Sim- ilarly, a movie profile generated from the posts associated to the movie. The proposed prototype resembles a content-based recommender sys- tem, where users are matched against recommended items. A small user study by Teevan et al. (2011) reports that 49% of users search while looking for information related to news, or to topics gaining popularity, and in general to “to keep up with events.” The analysis of a larger crawl of Twitter shows that about 85% of the Twitter posts are about headlines or persistent news (Kwak et al., 2010). As a result, 104
- 123. this abundance of news-related content makes Twitter the ideal source of information for the news recommendation task. Akcora et al. (2010) use Twitter to detect abrupt opinion changes. Based on an emotion-word corpus, the proposed algorithm detects opinion changes, which can be related to publication of some interesting news. No actual automatic linking to news is produced. The system proposed by Phelan et al. (2011) is a content-based approach that uses tweets to rank news using tf·idf. A given a set of tweets, either public or of a friend, is used to build a user profile, which is matched against the news coming from a set of user-defined RSS feeds. McCreadie et al. (2010) show that, even if useful, URL links present in blog posts may not be suf- ficient to identify interesting news due to their sparsity. Their approach exploits user posts as if they were votes for the news on a given day. The association between news and posts is estimated by using a divergence from randomness model. They show that a gaussian weighting scheme can be used profitably to predict the importance of a news on a given day, given the posts of a few previous days. Our approach pursues the same direction, with the goal of exploit- ing Twitter posts to predict news of interest. To this end, rather than analyzing the raw text of a tweet, we chose to extract the entities dis- cussed in tweets. Indeed, Twitter highlights in its Web interfaces the so called trending topics, i.e., set of words occurring frequently in recent tweets. Asur et al. (2011) crawled all the tweets containing the keywords identifying a Twitter trending topic in the 20 minutes before the topic is detected by Twitter. The authors find that the popularity of a topic can be described as a multiplicative growth process with noise. Therefore the cumulative number of tweets related to a trending topic increases linearly with time. Kwak et al. (2010) conduct an interesting study on a large crawl of Twitter, and analyze a number of features and phenomena across the social network. We highlight a few interesting findings. After the initial break-up, the cumulative number of tweets of a trending topic increases linearly, as suggested by Asur et al. (2011), and independently of the number of users. Almost 80% of the trending topics have a single activity 105
- 124. period, i.e., they occur in a single burst, and 93% of such activity periods last less than 10 days. Also, once a tweet is published, half of its re-tweets occur within an hour and 75% within one day. Finally, once re-tweeted, tweets quickly spread four hops away. These studies confirm the fast information spreading occurring on Twitter. A basic approach for building topic-based user profiles from tweets is proposed by Michelson and Macskassy (2010). Each capitalized non- stopword is considered an entity. The entity is used to query Wikipedia and the categories of the retrieved page are used to update the list of topics of interest for the user who authored the tweet. Abel et al. (2011) propose a more sophisticated user model to support news recommendation for Twitter users. They explore different ways of modeling use profiles by using hashtags, topics or entities and conclude that entity based modeling gives the best results. They employ a simple recommender algorithm that uses cosine similarity between user profiles and tweets. The authors recommend tweets containing news URLs and re-tweets are used as ground truth. Based on these results, we choose to use Wikipedia to build an entity based user model. We use the SPECTRUM system (Paranjpe, 2009) to map every single tweet to a bag of entities, each corresponding to a Wikipedia page. We apply the same entity extraction process to the stream of news with the goal of overcoming the vocabulary mismatch problem. Our pro- posed model borrows from the aforementioned works by exploiting a blend of content-based and social-based profile enrichment. In addition it is able to discover emerging trends on Twitter by measuring entity popularity and taking into account aging effects. Finally, we propose to learn the ranking function directly from available data. 5.3 Problem definition and model Our goal is to harness the information present in tweets posted by users and by their social circles in order to make relevant and timely recom- mendation of news articles. We proceed by introducing our notation and define formally the problem that we consider in this work. For quick 106
- 125. Table 5.1: Table of symbols. Symbol Definition N = {n0, n1, . . .} Stream of news ni i-th news article T = {t0, t1, . . .} Stream of tweets ti i-th tweet U = {u0, u1, . . .} Set of users Z = {z0, z1, . . .} Set of entities τ(ni) Timestamp of the i-th news article ni τ(ti) Timestamp of the i-th tweet ti c(ni) Timestamp of the click on ni S Social network matrix S∗ Social-influence network matrix A User × tweet authorship matrix T Tweet × entity relatedness matrix N Entity × news relatedness matrix M = T · N Tweet × news relatedness matrix Γ = A · M User × news content relatedness Σ = S∗ · A · M User × news social relatedness Z Entity popularity Π = Z · N News popularity Rτ (u, n) Ranking score of news n for user u at time τ reference, our notation is also summarized in Table 5.1. Definition 2 (News stream). Let N = {n0, n1, . . .} be an unbounded stream of news arriving from a set of news sources, where news article ni is published at time τ(ni). Definition 3 (Tweet stream). Let T = {t0, t1, . . .} be an unbounded stream of tweets arriving from the set of Twitter users, where tweet ti is published at time τ(ti). Problem 3 (News recommendation problem). Given a stream of news N, a set of users U = {u0, u1, . . .} and their stream of tweets T , find the top-k most relevant news for user u ∈ U at time τ. We aim at exploiting the tweet and news streams to identify news 107
- 126. of general interest, but also at exploiting a Twitter-based user profile to provide personalized recommendations. That is, for any user u ∈ U at any given time τ, the problem requires to rank the stream of past news in N according to a user-dependent relevance criteria. We also aim at incorporating time recency into our model, so that our recommendations favor the most recently published news articles. We now proceed to model the factors that affect the relevance of news for a given user. We first model the social-network aspect. In our case, the social component is induced by the Twitter following relationship. We define S to be the social network adjacency matrix, were S(i, j) is equal to 1 divided by the number of users followed by user ui if ui follows uj, and 0 otherwise. We also adopt a functional ranking (Baeza-Yates et al., 2006) that spreads the interests of a user among its neighbors recursively. By limiting the maximum hop distance d, we define the social influence in a network as follows. Definition 4 (Social influence S∗ ). Given a set of users U = {u0, u1, . . .}, organized in a social network where each user may express an interest to the content published by another user, we define the social influence model S∗ as the |U| × |U| matrix where S∗ (i, j) measures the interest of user ui to the content generated by user uj and it is computed as S∗ = i=d i=1 σi Si , where S is the row-normalized adjacency matrix of the social network, d is the maximum hop-distance up to which users may influence their neighbors, and σ is a damping factor. Next we model the profile of a user based on the content that the user has generated. We first define a binary authorship matrix A to capture the relationship between users and the tweets they produce. Definition 5 (Tweet authorship A). Let A be a |U|×|T | matrix where A(i, j) is 1 if ui is the author of tj, and 0 otherwise. The matrix A can be extended to deal with different types of relation- ships between users and posts, e.g., weigh differently re-tweets, or likes. 108
- 127. In this work, we limit the concept of authorship to the posts actually written by the user. It is worth noting that a tweet stream for a user is composed of tweets authored by the user and by people in the social neighborhood of the user. This is a generalization of the “home timeline” as known in Twitter. We observe that news and tweets often happen to deal with the same topic. Sometimes a given topic is pushed into Twitter by a news source, and then it spread throughout the social network. However sometimes a given topic is first discussed by Twitter users, and it is later reflected in the news, which may or may not be published back on Twitter. In both cases, it is important to discover which are the current trending topics in order to promptly recommend news of interest. We model the rela- tionship between tweets and news by introducing an intermediate layer between the two streams. This layer is populated by what we call entities. Definition 6 (Tweets-to-news model M). Let N be a stream of news, T a stream of tweets, and Z = {z0, z1, . . .} a set of entities. We model the relationship between tweets and news as a |T | × |N| matrix M, where M(i, j) is the relatedness of tweet ti to news nj, and it is computed as M = T · N, where T is a |T | × |Z| row-wise normalized matrix with T(i, j) representing the re- latedness of tweet ti to entity zj; N is a |Z|×|N| column-wise normalized matrix with N(i, j) representing the relatedness of entity zi to news nj. The set of entities Z introduces a middle layer between the stream of news and the stream of tweets that allows us to generalize our analysis. First, this layer allows to overcome any vocabulary mismatch problem between the two streams, since the streams are mapped onto the entity space. Second, rather than monitoring the relevance of a specific news or a tweet, we propose to measure the relevance of an entity. A number of techniques can be used to extract entities from news and tweets. A naïve approach is to let each term in the dictionary play 109
- 128. the role of an entity. In this case T(t, z) can be estimated as the number of occurrences of the term z in the tweet t, or as a tf·idf score, and similarly for N. Alternatively, probabilistic latent semantic indexing can map tweets and news onto a set of latent topics (Hofmann, 1999). In this work we follow a third approach: we use an existing entity- extraction system. In particular we use the SPECTRUM system, which was proposed by Paranjpe (2009). Given any fragment of text, the SPEC- TRUM system identifies entities related to Wikipedia articles. Therefore, we assume that Z consists of the set of all titles of Wikipedia articles. This choice has some interesting advantages. First, once an entity is detected, it is easy to propose a meaningful label to the user. Second, it allows to include additional external knowledge into the ranking, such as ge- ographic position, categorization, number of recent edits by Wikipedia users. Although we choose to use Spectrum, we note that our model is independent of the specific entity extraction technique employed. Example. Consider the following tweet by user KimAKelly: “Miss Lib- erty is closed until further notice.” The words “Miss Liberty” are mapped to the entity/Wikipedia page Statue of Liberty, which is an interesting topic, due to the just announced renovation. This allows to rank high news regarding the Statue of Liberty, e.g. “Statue of Liberty to Close for One Year after 125th Anniversary” by Fox news. Potentially, since the Wikipedia page is geo-referenced, it is possible to boost the ranking of the news for users living nearby, or interested in the entity New York. Example. Consider the following tweet by user NASH55GARFIELD: “We don’t know how we’re gonna pay social security benefits to the el- derly & we’re spending 27.25 mill $ to renovate the Statue of Liberty!!!”. The following entities/Wikipedia pages are extracted: welfare (from “so- cial benefits”), social security and Statue of Liberty. This entity extraction suggests that news regarding the announced Statue of Liberty renova- tion, or the U.S. planned medicare cuts are of interests to the user. The three matrices S∗ , A, M can be used to measure the relatedness of the news in N to the tweets posted by a user or her social neighborhood. Definition 7 (Content-based relatedness Γ). Given the tweet authorship ma- trix A and the tweets-to-news model M for a stream of news N and a stream of 110
- 129. tweets T authored by users U, the relatedness between U and N is defined as Γ = A · M, where Γ is a |U| × |N| matrix, where Γ(ui, nj) is the relevance of news nj for user ui. According to the definition of Γ, a news article nj is relevant for user ui, if the news article discusses entities that have been discussed in the past by the user in her own tweets. Definition 8 (Social-based relatedness Σ). Given the tweet authorship ma- trix A, the tweets-to-news model M, and the social network S for a stream of news N and a stream of tweets T authored by users U, the relatedness between U and N is defined as Σ = S∗ · A · M, where Σ is a |U| × |N| matrix, where Σ(ui, nj) is the relevance of news nj for user ui. According to the definition of social-based relatedness Σ, the rele- vance of a news article is computed by taking into account the tweets authored by neighboring users. The matrices Γ and Σ measure content-based similarity, with no ref- erence to popularity or freshness of tweets, news articles, and entities. In order to provide timely recommendations and catch up with trending news, we introduce a popularity component, which combines the “hot- ness” of entities in the news stream and the tweet stream. Definition 9 (Entity-based news popularity Π). Given a stream of news N, a set of entities Z, and their relatedness matrix N, the popularity of N is defined as Π = Z · N, where Z is a row-wise vector of length |Z| and Z(i) is a measure of the popular- ity of entity zi. The resulting Π is a row-wise vector of length |N|, where Π(j) measures the popularity of the news article nj. The vector Z holds the popularity of each entity zi. The counts of the popularity vector Z need to be updated as new entities of interest arise in the news stream N and the tweet stream T . An important aspect 111
- 130. in updating the popularity counts is to take into account recency: new entities of interest should dominate the popularity counts of older enti- ties. In this work, we choose to update the popularity counts using an exponential decay rule. We discuss the details in Section 5.3.1. However, note that the popularity update is independent of our recommendation model, and any other decaying function can be used. Finally, we propose a ranking function for recommending news arti- cles to users. The ranking function is linear combination of the scoring components described above. We plan to investigate the effect of non- linear combinations in the future. Definition 10 (Recommendation ranking Rτ (u, n)). Given the components Στ , Γτ and Πτ , resulting form a stream of news N and a stream of tweets T authored by users U up to time τ, the recommendation score of a news article n ∈ N for a user u ∈ U at time τ is defined as Rτ (u, n) = α · Στ (u, n) + β · Γτ (u, n) + γ · Πτ (n), where α, β, γ are coefficients that specify the relative weight of the components. At any given time, the recommender system produces a set of news recommendation by ranking a set of candidate news, e.g., the most re- cent ones, according to the ranking function R. To motivate the pro- posed ranking function we note similarities with popular recommenda- tion techniques. When β = γ = 0, the ranking function R resembles collaborative filtering, where user similarity is computed on the basis of their social circles. When α = γ = 0, the function R implements a content-based recommender system, where a user is profiled by the bag- of-entities occurring in the tweets of the user. Finally, when α = β = 0, the most popular items recommended, regardless of the user profile. Note that Σ, Γ, Π and R are all time dependent. At any given time τ the social network and the set of authored tweets vary, thus affecting Σ and Γ. More importantly, some entities may abruptly become popular, hence of interest to many user. This dependency is captured by Π. While the changes in Σ and Γ derive directly from the tweet stream T and the social network S, the update of Π is non-trivial, and plays a fundamental role in the recommendation system that we describe in the next section. 112
- 131. 5.3.1 Entity popularity We complete the description of our model by discussing the update of the entity popularity counts. We motivate our approach by empirically observing how the user interest for particular entities decays over time. -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 M ay-01 h20M ay-02 h00M ay-02 h04M ay-02 h08M ay-02 h12M ay-02 h16M ay-02 h20M ay-03 h00M ay-03 h04M ay-03 h08 news twitter clicks Figure 5.3: Cumulative Osama Bin Laden trends (news, Twitter and clicks). Figure 5.3 shows the cumulative distribution of occurrences for the same entity of Figure 5.1. By using cumulative distribution, the fact the entity appears much earlier in Twitter than in the news becomes more evident. If we consider the number of clicks on news as a surrogate of user interest, we notice that with a delay of about one day the entity re- ceives a great deal of attention. This delay is probably due to the fact that the users have not been informed about the event yet. On the other hand, we observe that after two days the number of clicks drop, possibly the interest of users has been saturated or diverted to other events. 113
- 132. 1 10 100 1 10 100 1000 10000 Minutes News-click delay Figure 5.4: News-click delay distribution. We note that the example above is not an exception, rather it describes the typical behavior of users with respect to reading news articles online. Figure 5.4 shows the scatter plot of the distribution of delay between the time that news articles are published the when they are clicked by users. The figure considers all the news articles and all the clicks in our dataset as described in Section 5.6.1. Only a very small number of news is clicked within the first hour from their publication. Nonetheless, 76.7% of the clicks happen within one day (1440 minutes) and 90.1% within two days (2880 minutes). Anal- ogous observations can be made by looking at Figure 5.5, which shows the cumulative distribution of the delay and resembles a typical Pareto distribution. The slope of the curve is very steep up to about 2000 min- utes (33 hours), however it flattens out quite rapidly soon after. 114
- 133. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Minutes News-click delay Figure 5.5: Cumulative news-click delay distribution. From these empirical observations on the delay between news pub- lishing and user clicking we can draw the following conclusions: 1. The increase in the number of tweets and news related to a given entity can be used to predict the increase of interest of the users. 2. News become stale after two days. The first observation motivates us to inject a popularity component in our recommendation model. The second observation suggests updating popularity scores using a decaying function. We choose an exponentially- decaying function, which has the advantage of allowing to count effi- ciently frequent items in the data stream model. This choice allows to monitor entity popularity in high-speed data streams by using only a limited amount of memory (Cormode et al., 2008). 115
- 134. Definition 11 (Popularity-update rule). Given a stream of news N and a stream of tweets T at time τ, the popularity vector Z is computed at the end of every time window of fixed width ω as follows Zτ = λZτ−1 + wT HT + wN HN . The vectors HT and HN are estimates of the expected number of mentions of the entity occurring in tweets and news, respectively, during the latest time window. They are also called hotness coefficients. The weights wT and wN measure the relative impact of news and tweets to the popularity count, and λ < 1 is an exponential forgetting factor. The popularity-update rule has the effect of promptly detecting en- tities becoming suddenly popular, and spreading this popularity in the subsequent time windows. According to our experimental evidence, we fix λ so that a signal is becomes negligible after two days. We set both coefficients wT and wN to 0.5 to give equal weight to tweets and news. Asur et al. (2011) show that the number of tweets for a trending topic grows linearly over time. So we compute the expected counts of the entity in tweets and news HT and HN by using the first order derivative of their cumulative counts, measured at the last time window τ − 1. 5.4 System overview Figure 5.6 shows a general overview of the T.REX system. T.REX main- tains a user model for each user that is composed by the content related- ness and social relatedness components. Conceptually both components process tweets at high speed to extract and count entities. This operation can be done efficiently and in parallel at high speed. Efficiently keeping frequency moments in a stream is a classical problem in the literature of streaming algorithms (Alon et al., 1999). The social component also holds truncated PageRank values for the followees of each users. These values are used to weight the importance of the followee profile when computing recommendation scores for the user. Truncated PageRank values can be updated periodically, or when the social graph has been modified more than a given threshold. 116
- 135. tweets User tweets Followee tweets Followee tweets Followee tweets twitter articles news T.Rex User Model Σ Γ Π Personalized ranked list of news articles Figure 5.6: Overview of the T.REX system. PageRank is a typical batch operation and can be easily implemented in MR. Given that we use a truncated version of PageRank, this compu- tation is even cheaper because the values can spread only d hops away, therefore convergence will be faster. Parameters for the ranking function can be computed offline and updated likewise in a batch fashion. The users can possibly be clustered into groups and different parameters can be learned for each group. We leave the study of the effects of clustering for future work. Learning the parameters and the potential clustering are best seen as offline processes, given that the general preferences of the user are not supposed to change too rapidly. However processing high speed streams is a poor fit for MR. High speed counting is necessary both for the user model and for entity popu- larity. Even though MR has been extended to deal with incremental and continuous computations (Condie et al., 2009), there are more natural matches for computing on streams. One reason is that the fault tolerance guarantees of MR are too strong in this case. We would rather loose some tweets than wait for them to be reprocessed upon a crash, as long as the system is able to keep running. Freshness of data is a key property to preserve when mining streams, even at the cost of some accuracy. Therefore we propose to use the actors model to parallelize our sys- 117
- 136. tem (Agha, 1986). In particular, we describe how to implement it on S4. We use two different type of PEs to update the model: one for the con- tent component and one for entity popularity. The social component can be implemented by aggregating the values from various content compo- nents with pre-computed weights, so it does not need a separate PE. The weights can be updated in batches and computed in MR. A content PE receives tweets keyed on the author, extracts entities from the tweets and updates the counts for the entities seen so far. Then it sends messages keyed on the entity to popularity PEs in order to update their entity popularity counts. The entity extraction operation is performed also on incoming news by using a keyless PE. This PE just performs entity extraction on the in- coming news articles and forwards the mention counts downstream. The news articles with the extracted entities are kept in a pool as long as they do not become stale, after which they are discarded. A popularity PE receives entity count updates keyed on the entity. It updates its own counts by using the timestamp of the mention and an efficient procedure for exponentially decayed counters Cormode et al. (2008). As popularity is updated at fixed intervals, caching and batch- ing can be used to reduce the network load of the system. For instance updates can be sent only at time window boundaries. Figure 5.7 depicts an overview of the ranking process at query time. When the user logs into the system, the pool of news articles is ranked according to the user model model and the entity popularity informa- tion. The search for relevant news can be speeded up by employing an inverted index of the entities in each news, and indeed the process is very similar to answering a query in a Web search engine. All the standard techniques for query processing found in the infor- mation retrieval literature can be used. For example, it is possible to employ early exit optimizations (Cambazoglu et al., 2010). Ranking of news can proceed in parallel at different PEs, and finally only the top-k news articles from each PE need to be aggregated again at a single place. 118
- 137. Personalized ranked list of news articles Entity-based user model at login time Dynamic news pool News index by entity Popular entities ΣΓ Π Ranking function Figure 5.7: T.REX news ranking dataflow. 5.5 Learning algorithm The next step is to estimate the parameters of the relevance model that we developed in the previous section. The parameters consist of the co- efficients α, β, γ used to adjust the relative weight of the components of the ranking function Rτ . Another parameter is the damping factor used in the computation of social influence, but we empirically observed that it does not influence the results very much, so we used a default value of σ = 0.85 common in PageRank. We consider only direct neighbors by setting the maximum hop distance d = 1. This choice is for practical reasons, since crawling Twitter is rate limited and thus very slow. Our approach is to learn the parameters of the model by using train- ing data obtained from action logs. In particular, we use click-log data from Yahoo! toolbar as a source of user feedback, The Yahoo! toolbar anonymously collects clicks of several millions of users on the Web, in- cluding clicks on news. Our working hypothesis is that a high-quality news recommender ranks high the news that will be clicked by users. We 119
- 138. actually formulate our recommendation task according to the learning- to-rank framework (Joachims, 2002). Consider a user u ∈ U and a news article n ∈ N with publication timestamp τ(n) ≤ τ, where τ is the current time. We say that the news article n should be ranked in the i-th position of the recommendation list for user u, if it will be the i-th article to be clicked in the future by user u. This formulation allows to define precedence constraints on the rank- ing function Rτ . Let c(n) be the time at which the news n is clicked, and let c(n) = +∞ if n is never clicked. At time τ, for two news ni, nj with τ(ni) ≤ τ and τ(nj) ≤ τ, we obtain the following constraint: If τ ≤ c(ni) < c(nj) then Rτ (u, ni) > Rτ (u, nj). (5.1) The click stream from Yahoo! toolbar identifies a large number of con- straints according to Equation (5.1) that the optimal ranking function must satisfy. As for the learning-to-rank problem Joachims (2002), find- ing the optimal ranking function is an NP-hard problem. Additionally, considering that some of the constraints could be contradictory, a feasi- ble solution may not exist. As usual, the learning problem is translated to a Ranking-SVM optimization problem. Problem 4 (Recommendation Ranking Optimization). Minimize: V −→ω ≡ α, β, γ , −→ ξ = 1 2 −→ω 2 + C ξijτ Subject to: Rτ (u, ni) > Rτ (u, nj) + 1 − ξijτ for all τ, ni ∈ N, nj ∈ N such that τ(ni) ≤ τ, τ(nj) ≤ τ, τ ≤ c(ni) < c(nj) ξijτ ≥ 0 As shown by Joachims (2002), this optimization problem can be solved via classification SVM. In the following sections, we show how to gener- ate the training set of the SVM classifier in order to keep a reasonably low amount of training instances, so as to speed-up convergence and support the scalability of the solution. 120
- 139. 5.5.1 Constraint selection The formulation of Problem 4 includes a potentially huge number of con- straints. Every click occurring after time τ on a news n, generates a new constraints involving n and every other non-clicked news published be- fore time τ. Such a large number of constraints also includes relation- ships on “stale” news articles, e.g., a non-clicked news article published weeks or months before τ. Clicks are the signals driving the learning pro- cess. So it is important to select pairs of clicked news articles that elim- inate biases such as the one caused by stale news articles. Clearly, the more constraints are taken into consideration during the learning pro- cess, the more robust is the final model. On the other hand, increasing the number of constraints affects the complexity of the minimization al- gorithm. We propose the following strategy in order to select only the most interesting constraints and thus simplify the optimization problem. First, we evaluate the ranking function only at the time instants when a click happens. This selection does not actually change the set of con- straints of Problem 4, but it helps in the generation of the constraints by focussing on specific time instants. If the user u clicks at the news article ni at time c(ni), then the news article ni must be the most relevant at that time. The following condition must hold. Rc(ni)(u, ni) > Rc(ni)(u, nj) + 1 − ξijc(ni) for all nj ∈ N such that τ(nj) ≤ c(ni). (5.2) Whenever a click occurs at time c(ni), we add a set of constraint to the ranking function such that the clicked news article gets the largest score among any other news article published before time c(τ). Second, we restrict the number of news articles to be compared with the clicked one. If a news article was published a long time before the click, then it can be easily filtered out, as it would not help the learning process. As we have shown in Section 5.3.1, users lose interest into news articles after a time interval τ of two days. We can make use of this 121
- 140. threshold into Equation (5.2) as follows: Rc(ni)(u, ni) > Rc(ni)(u, nj) + 1 − ξijc(ni) for all nj ∈ N [c(ni) − τ, c(ni)] , (5.3) where N [c(ni) − τ, c(ni)] is the set of news articles published between time c(ni) − τ and c(ni). Finally, we further restrict N [c(ni) − τ, c(ni)] by considering only the articles which that are relevant according to at least one of the three score components Στ , Γτ , Πτ . Let Top(k, χ, τa, τb) be the set of k news articles with largest rank in the set N [τa, τb] according to the score component χ. We include into the optimization Problem 4 only the constraints: Rc(ni)(u, ni) > Rc(ni)(u, nj) + 1 − ξijc(ni) for all nj s.t. nj ∈ Top k, Σc(ni), c(ni) − τ, c(ni) or nj ∈ Top k, Γc(ni), c(ni) − τ, c(ni) or nj ∈ Top k, Πc(ni), c(ni) − τ, c(ni) . (5.4) By setting k = 10 we are able to reduce the number of constraints from more than 25 million to approximately 250 thousand, thus significantly reducing the training time of the learning algorithm. 5.5.2 Additional features The system obtained by learning the model parameters using the SVM- Rank method is named T.REX, and forms our main recommender. Ad- ditionally, we attempt to improve the accuracy of T.REX by incorporat- ing more features. To build this improved recommender we use exactly the same learning framework: we collect more features from the same training dataset and we learn their importance using the SVM-Rank al- gorithm. We choose three additional features: age, hotness and click count, which we describe below. The age of a news article n is the time elapsed between the current time and the time n was published, that is, τ − τ(n). The hotness of a news article is a set of features extracted from the vectors HT and HN , which keep the popularity counts for the entities in 122
- 141. our model. For each news article n we compute the average and stan- dard deviation of the vectors HT and HN over all entities extracted from article n. This process gives us four hotness features per news article. Finally, the click count of a news article is simply the number of times that the article has been clicked by any users in the system up to time τ. The system that we obtain by training our ranking function on these additional features is called T.REX+. 5.6 Experimental evaluation 5.6.1 Datasets 1 10 100 1000 10000 100000 1e+06 1e+07 10 100 1000 10000 100000 Count Entity Distribution Cumulative Figure 5.8: Distribution of entities in Twitter. To build our recommendation system we need the following sources of information: Twitter stream, news stream, the social network of users, 123
- 142. 1 10 100 1000 10000 100000 1e+06 10 100 1000 10000 Count Entity Distribution Cumulative Figure 5.9: Distribution of entities in news. and click-through data. We extract this information from three different data sources: Twitter, Yahoo! news, and Yahoo! toolbar, respectively. Twitter: We obtain tweets from Twitter’s public API by crawling users’ timelines. We collect all tweets posted during May 2011 by our 3, 214 target users (identified as described below). We also collect a random sample of tweets to track entity popularity across all Twitter. We extract entities from tweets using the Spectrum method described by Paranjpe (2009). Overall we obtain about 1 million tweets in English, for which we are able to extract entities. Figure 5.8 shows the distribution of entities in the Twitter dataset. The curve has a truncated power law shape. Yahoo! news: We collect all news articles aggregated in the English site of Yahoo! news during May 2011. From the news articles we extract entities by using again the Spectrum algorithm. Overall we have about 28.5 million news articles, from which we keep only the articles that contain 124
- 143. at least one entity contained in one of the tweets. In total we obtain about 40 thousand news articles. Figure 5.9 shows the distribution of entities in the Yahoo! news dataset. The shape of the distribution is similar to the one of Twitter, a truncated power law distribution. Yahoo! toolbar: We collect click information from the Yahoo! toolbar logs. The Yahoo! toolbar is a browser add-on that provides a set of brows- ing functionalities. The logs contain information about the browsing be- havior of the users who have installed the toolbar, such as, user cookie id, url, referral url, event type, and so on. We collect all toolbar data oc- curring in May 2011. We use the first 80% in chronological order of the toolbar clicks to train our system. Using a simple heuristic we identify a small set of users for whom we can link their toolbar cookie id, with their Twitter user id. The heuristic is to identify which Twitter account a user is visiting more often, dis- carding celebrity accounts and non-bijective mappings. The underlying assumption is that users visit more often their own accounts. In total we identify of set U0 of 3,214 test users. The dataset used in this work is the projection of all the data sources on the users of the set U0, that is, for all the users in U0 we collect all their tweets and all their clicks on Yahoo! news. Additionally, by employing snowball sampling on Twitter we ob- tain the set of users U1 who are followed by the set of users U0. Then, by collecting all the tweets of the users in U1, we form the social component for our set of users of interest U0. 5.6.2 Test set Evaluating a recommendation strategy is a complex task. The ideal eval- uation method is to deploy a live system and gather click-through statis- tics. While such a deployment gives the best accuracy, it is also very expensive and not always feasible. User studies are a commonly used alternative evaluation method. However, getting judgements from human experts does not scale well to a large number of recommendations. Furthermore, these judgement are often biased because of the small sample sizes. Finally, user studies 125
- 144. cannot be automated, and they are impractical if more than one strategy or many parameters need to be tested. For these reasons, we propose an automated method to evaluate our recommendation algorithm. The proposed evaluation method exploits the available click data collected by the Yahoo! toolbar, and it is similar in spirit with the learning process. Given a stream of news and a stream of tweets for the user, we identify an event that a user clicks at a news article n∗. Assume that such a click occurs at time τ = c(n∗). Suppose the user just logged in the system at time τ. Then the recommendation strategy should rank the news article n∗ as high as possible. To create a test instance, we collect all news articles that have been published within the time interval [τ − τ∗ , τ], and select a subset as de- scribed by Equation (5.4): we pick the news with largest scores according to the components of content, social, popularity, and number of clicks un- til time τ. In total we generate a pool of k = 1,000 candidate news. All these news articles are ranked using our ranking function Rτ , and we then examine what is the ranking of the article n∗ in the list. We use the last 20%, in chronological order, of the Yahoo! toolbar log to test the T.REX and T.REX+ algorithms, as well as all the baselines. 5.6.3 Evaluation measures Evaluating a ranking of items is a standard problem in information re- trieval. In our setting we have only one correct answer per ranking — the news article n∗ clicked by the user — and we care about the position of this item in the ranking, which we evaluate using the Mean Reciprocal Rank (MRR) measure Voorhees (1999): MRR = 1 |Q| Q i=1 1 r(ni ∗) , where r(ni ∗) is the rank of the news article ni ∗ in the i-th event of the eval- uation and Q is the set of all tests. The MRR measure is commonly used to evaluate question-answering systems, where only the first correct an- swer matters. MRR gives higher scores to correct results that are higher 126
- 145. in the ranking and reduces the importance of correct predictions in the lower parts of the ranking. We also compute the precision of our system at different levels. For our task we define the precision-at-k (P@k) as the fraction of rankings in which the clicked news is ranked in the top-k positions. We compute P@k for k = 1, 5, and 10. There are cases in which the sparsity of the data prevents our system from providing recommendations. Therefore, we also evaluate the cov- erage of our recommendations. We define the coverage as the fraction of clicks for which we were able to provide some recommendation. Finally, we note that when the user clicks on a news, the user is ac- tually expressing interest in the entities mentioned in the news. We can argue that if a user clicks on a report on Fukushima from CNN, the user might equally be interested in a report on the same topic from BBC. In this case, we would like to predict the entities that the user is interested in, rather than the news articles themselves. We use Jaccard overlap between the sets of entities mentioned in two news articles to measure the similarity between the articles themselves. We compute the similarity between each news article in the ranking and the clicked news. Then, we assign a relevance level to each news by bin- ning the computed similarity into five levels. This gives rise to a ranking task with multiple levels of relevance. We use Discounted Cumulated Gain (DCG) (Järvelin and Kekäläinen, 2002) to measure the performance of the strategies on this newly defined task: DCG [i] = G [i] if i = 1; DCG [i − 1] + G[i] log2i if i > 1, where G[i] is the relevance of the document at position i in our ranking. We compute the DCG for the top 20 results averaged over all the rank- ings produced. If a strategy is not able to produce a ranking, we pad the ranking with non-relevant documents. 127
- 146. Table 5.2: MRR, precision and coverage. Algorithm MRR P@1 P@5 P@10 Coverage RECENCY 0.020 0.002 0.018 0.036 1.000 CLICKCOUNT 0.059 0.024 0.086 0.135 1.000 SOCIAL 0.017 0.002 0.018 0.036 0.606 CONTENT 0.107 0.029 0.171 0.286 0.158 POPULARITY 0.008 0.003 0.005 0.012 1.000 T.REX 0.107 0.073 0.130 0.168 1.000 T.REX+ 0.109 0.062 0.146 0.189 1.000 5.6.4 Baselines We compare our system with other five ranking baselines: RECENCY: it ranks news articles by time of publication (most recent first); CLICKCOUNT: it ranks news articles by click count (highest count first); SOCIAL: it ranks news articles by using T.REX with β = γ = 0; CONTENT: it ranks news articles by using T.REX with α = γ = 0; POPULARITY: it ranks news articles by using T.REX with α = β = 0. 5.6.5 Results We report MRR, precision and coverage results in Table 5.2. The two variants of our system, T.REX and T.REX+, have the best results overall. T.REX+ has the highest MRR of all the alternatives. This result means that our model has a good overall performance across the dataset. CON- TENT has also a very high MRR. Unfortunately, the coverage achieved by the CONTENT strategy is very low. This issue is mainly caused by the sparsity of the user profiles. It is well know that most of Twitter users belong to the “silent majority,” and do not tweet very much. The SOCIAL strategy is affected by the same problem, albeit to a much lesser extent. The reason for this difference is that SOCIAL draws from a large social neighborhood of user profiles, instead of just one. So it 128
- 147. 0 2 4 6 8 10 12 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 AverageDCG Rank T.Rex+ T.Rex Popularity Content Social Recency Click count Figure 5.10: Average discounted cumulated gain on related entities. has more chances to provide a recommendation. The quality of the rec- ommendation is however quite low, probably because the social-based profile only is not able to catch the specific user interests. It is worth noting that in almost 20% of the cases T.REX+ was able to rank the clicked news in the top 10 results. Ranking by the CLICKCOUNT strategy is quite efficient despite being very simple. Interestingly, adding the CLICKCOUNT feature to our model does not improve the results sig- nificantly. In fact, the difference in P@10 between T.REX and T.REX+ is only about 2%. This suggests that the information contained in the click counts is already captured by our model, or cannot be effectively exploited by a linear combination. Figure 5.10 shows the DCG measure for the top 20 positions in the rankings. From the figure we can see that, compared to the other strate- gies, T.REX and T.REX+ are able to suggest more news articles about the same entities mentioned in the clicked news. This result is expected, as our system is specifically designed to exploit the concept of entity. 129
- 148. 5.7 Conclusions The real-time Web can provide timely information on important events, and mining it online with stream processing allows to yield maximum benefit from it. In this chapter we proposed an application to online news recommendation. Our goal is to help the user keep up with the torrent of news by providing personalized and timely suggestions. We described T.REX, an online recommender that combines stream and graph mining to harness the information available on Twitter. T.REX creates personalized entity-based user models from the information in the tweet streams coming from the user and his social circle, and further tracks entity popularity in Twitter and news streams. T.REX constantly updates the models in order to continuously provide fresh suggestions. We framed our problem as a click-prediction task and we tested our system on real-world data from Twitter and Yahoo! news. We combined the signals from the two streams by using a learning-to-rank approach with training data extracted from Yahoo! toolbar logs. T.REX is able to predict with good accuracy the news articles clicked by the users and rank them higher on average. Our results show that the real-time Web is a useful resource to build powerful predictors of user interest. 130
- 149. Chapter 6 Conclusions “In pioneer days they used oxen for heavy pulling, and when one ox couldn’t budge a log, they didn’t try to grow a larger ox.” Admiral Grace Hopper, developer of the first compiler. Data Intensive Scalable Computing is an emerging technology in the data analysis field that can be used to capitalize on massive datasets com- ing from the Web. In particular MapReduce and streaming are the two most promising emerging paradigms for analyzing, processing and mak- ing sense of large heterogeneous datasets. While MapReduce offers the capability to analyze large batches of stored data, streaming solutions of- fer the ability to continuously process unbounded streams of data online. “It is not who has the best algorithms that wins, it is who has more data” is a well known aphorism. The importance of big data is widely recog- nized both in academia and in industry, and the Web is the largest public data repository available. Information extracted from the Web has the potential to have a big impact in our society. Data on the Web is heterogeneous and is best modeled in different ways. To fully exploit the power of parallelism offered by DISC systems, algorithms need to take into account the characteristics of their input data. Therefore, designing algorithms for large scale Web mining is an interesting and challenging research goal. 131
- 150. In this thesis we have explored how to tackle the big data problem for the Web by employing Data Intensive Scalable Computing. This prob- lem has two sides. On the one hand we need effective methodologies to make sense of the complex relationships that underly data on the Web. On the other hand we need efficient techniques that enable processing of large datasets. This thesis sheds some light at the crossing of these two areas of research, and investigates the synergies and difficulties in performing large scale Web mining using Data Intensive Scalable Com- puting. Our work builds on previous research in Data Mining, Informa- tion Retrieval and Machine Learning to make sense of the complex data available on the Web. We also employ the products of Distributed Sys- tems and Database research to manage the Web-scale datasets. We have tackled three classical problems in Web mining and provided solutions for MapReduce and streaming. In Chapter 3 we addressed the issue of similarity on bags of Web pages. Finding similar items in a bag of documents is a challenging prob- lem that arises in many applications in the areas of Web mining. The size of Web-related problems mandates the use of parallel approaches in or- der to achieve reasonable computing times. We presented SSJ-2 and SSJ- 2R, two algorithms specifically designed for the MapReduce program- ming paradigm. We showed that designing efficient algorithms for MR is not trivial and requires careful blending of several factors to effectively capitalize on the available parallelism. We analyzed and compared our algorithms with the state-of-the-art theoretically and experimentally on a sample of the Web. SSJ-2R borrows from previous approaches based on inverted index, and embeds pruning strategies that have been used only in sequential algorithms so far. Designing algorithms specifically for MapReduce by rethinking classical algorithms gives substantial per- formance advantages over black box parallelization. By applying this principle SSJ-2R achieves scalability without sacrificing precision by ex- ploiting each MR phase to perform useful work. SSJ-2R outperforms the state-of-the-art for similarity join in MapReduce by almost five times. In Chapter 4 we explored graph b-matching and proposed its appli- cation to the distribution of user-generated content from Web 2.0 sites. 132
- 151. Our goal is to help users experience websites with large collections of user-generated content. We described STACKMR and GREEDYMR, two iterative MapReduce algorithms with different performance and qual- ity properties. These algorithms represent the first solution to the graph b-matching problem in MapReduce. They rely on the same base com- munication pattern for iterative graph mining in MR which can support a variety of algorithms and provides a scalable building block for graph mining in MR. Both algorithms have provable approximation guarantees and scale to massive datasets. In addition STACKMR provably requires only a poly-logarithmic number of MapReduce iterations. On the other hand GREEDYMR has a better approximation guarantee and allows to query the solution at any time. We evaluated our algorithms on two large real-world datasets from the Web and highlighted the tradeoffs between quality and performance between the two solutions. In Chapter 5 we investigated online news recommendation for real- time Web users. Our goal is to help the user keep up with the torrent of news by providing personalized and timely suggestions. We devised T.REX, an online recommender that combines stream and graph min- ing to harness the information available on Twitter. The proposed sys- tem processes all the incoming data online in a streaming fashion and is amenable to parallelization on stream processing engines like S4. This feature allows to provide always fresh recommendations and to cope with the large amount of input data. T.REX extracts several signals from the real-time Web to predict user interest. It is able to harnesses informa- tion extracted from user-generated content, social circles and entity pop- ularity in Twitter and news streams. Our results show that the real-time Web is a useful resource to build powerful predictors of user interest. The research results presented in this thesis open the way to some interesting questions that deserve further investigation. It is reasonable to ask whether all of the useful part of the Web can be modeled as bags, graphs, streams or a mix of these. Furthermore, the Web is highly dy- namic and changes rapidly. Therefore new kinds of data might require new models and new algorithms. On the other hand new DISC systems are emerging and they might provide a good fit for some of the algo- 133
- 152. rithms presented here, especially for graph and iterative computations. Finally, the algorithms presented in Chapter 3 and Chapter 4 can be gen- eralized to contexts different from the Web. Finding the limits of appli- cability of these algorithms is an interesting line of research. Some direct extensions of the present work are also worth of notice. For instance computing top-k and incremental versions of the similarity self-join problem, or exploring the effects of clustering users and employ- ing entity categories on the news recommendation problem. Finally, live deployments of the systems described in Chapter 4 and 5 could provide useful insight on the quality of the suggestions made. This would in turn open new spaces for further research on user engagement. We believe that the topic investigated in this thesis has the potential for great practical impact in our society. We hope that the contributions presented here will be valuable for the future researchers in the field. 134
- 153. Appendix A List of Acronyms API Application Programming Interface CERN European Council for Nuclear Research GPS Global Positioning System HOP Hadoop Online Prototype LHC Large Hadron Collider NAS Network Attached Storage P2P Peer-to-Peer RFID Radio-Frequency Identification SAN Storage Area Network SMP Symmetric Multi-Processor BSP Bulk Synchronous Parallel DAG Direct Acyclic Graph DBMS Database Management System DHT Distributed Hash Table 135
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