Classfication Basic.ppt

1
Classification Problem
Concepts and Techniques
Source: Jiawei Han, Micheline Kamber, and Jian Pei
University of Illinois at Urbana-Champaign &
Simon Fraser University
©2011 Han, Kamber & Pei. All rights reserved.

2
Classification: Basic Concepts
 Classification: Basic Concepts
 Decision Tree Induction
 Bayes Classification Methods
 Rule-Based Classification
 Model Evaluation and Selection
 Techniques to Improve Classification Accuracy:
Ensemble Methods
 Summary

3
 Classification
 predicts categorical class labels (discrete or nominal)
 classifies data (constructs a model) based on the training
set and the values (class labels) in a classifying attribute
and uses it in classifying new data
 Numeric Prediction
 models continuous-valued functions, i.e., predicts
unknown or missing values
 Typical applications
 Credit/loan approval:
 Medical diagnosis: if a tumor is cancerous or benign
 Fraud detection: if a transaction is fraudulent
 Web page categorization: which category it is
Prediction Problems: Classification vs.
Numeric Prediction

4
Decision Tree Induction: An Example
age?
overcast
student? credit rating?
<=30 >40
no yes yes
yes
31..40
fair
excellent
yes
no
age income student credit_rating buys_computer
<=30 high no fair no
<=30 high no excellent no
31…40 high no fair yes
>40 medium no fair yes
>40 low yes fair yes
>40 low yes excellent no
31…40 low yes excellent yes
<=30 medium no fair no
<=30 low yes fair yes
>40 medium yes fair yes
<=30 medium yes excellent yes
31…40 medium no excellent yes
31…40 high yes fair yes
>40 medium no excellent no
 Training data set: Buys_computer
 The data set follows an example of
Quinlan’s ID3 (Playing Tennis)
 Resulting tree:

5
Algorithm for Decision Tree Induction
 Basic algorithm (a greedy algorithm)
 Tree is constructed in a top-down recursive divide-and-
conquer manner
 At start, all the training examples are at the root
 Attributes are categorical (if continuous-valued, they are
discretized in advance)
 Examples are partitioned recursively based on selected
attributes
 Test attributes are selected on the basis of a heuristic or
statistical measure (e.g., information gain)
 Conditions for stopping partitioning
 All samples for a given node belong to the same class
 There are no remaining attributes for further partitioning –
majority voting is employed for classifying the leaf
 There are no samples left

Brief Review of Entropy

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m = 2

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Attribute Selection Measure:
Information Gain (ID3/C4.5)
 Select the attribute with the highest information gain
 Let pi be the probability that an arbitrary tuple in D belongs to
class Ci, estimated by |Ci, D|/|D|
 Expected information (entropy) needed to classify a tuple in D:
 Information needed (after using A to split D into v partitions) to
classify D:
 Information gained by branching on attribute A
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Attribute Selection: Information Gain
 Class P: buys_computer = “yes”
 Class N: buys_computer = “no”
means “age <=30” has 5 out of
14 samples, with 2 yes’es and 3
no’s. Hence
Similarly,
age pi ni I(pi, ni)
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31…40 4 0 0
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Computing Information-Gain for
Continuous-Valued Attributes
 Let attribute A be a continuous-valued attribute
 Must determine the best split point for A
 Sort the value A in increasing order
 Typically, the midpoint between each pair of adjacent values
is considered as a possible split point
 (ai+ai+1)/2 is the midpoint between the values of ai and ai+1
 The point with the minimum expected information
requirement for A is selected as the split-point for A
 Split:
 D1 is the set of tuples in D satisfying A ≤ split-point, and D2 is
the set of tuples in D satisfying A > split-point

10
Gain Ratio for Attribute Selection
(C4.5)
 Information gain measure is biased towards attributes with a
large number of values
 C4.5 (a successor of ID3) uses gain ratio to overcome the
problem (normalization to information gain)
 GainRatio(A) = Gain(A)/SplitInfo(A)
 Ex.
 gain_ratio(income) = 0.029/1.557 = 0.019
 The attribute with the maximum gain ratio is selected as the
splitting attribute
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Gini Index (CART, IBM
IntelligentMiner)
 If a data set D contains examples from n classes, gini index,
gini(D) is defined as
where pj is the relative frequency of class j in D
 If a data set D is split on A into two subsets D1 and D2, the gini
index gini(D) is defined as
 Reduction in Impurity:
 The attribute provides the smallest ginisplit(D) (or the largest
reduction in impurity) is chosen to split the node (need to
enumerate all the possible splitting points for each attribute)
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Computation of Gini Index
 Ex. D has 9 tuples in buys_computer = “yes” and 5 in “no”
 Suppose the attribute income partitions D into 10 in D1: {low,
medium} and 4 in D2
Gini{low,high} is 0.458; Gini{medium,high} is 0.450. Thus, split on the
{low,medium} (and {high}) since it has the lowest Gini index
 All attributes are assumed continuous-valued
 May need other tools, e.g., clustering, to get the possible split
values
 Can be modified for categorical attributes
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Comparing Attribute Selection Measures
 The three measures, in general, return good results but
 Information gain:
 biased towards multivalued attributes
 Gain ratio:
 tends to prefer unbalanced splits in which one partition is
much smaller than the others
 Gini index:
 biased to multivalued attributes
 has difficulty when # of classes is large
 tends to favor tests that result in equal-sized partitions
and purity in both partitions

14
Other Attribute Selection Measures
 CHAID: a popular decision tree algorithm, measure based on χ2 test for
independence
 C-SEP: performs better than info. gain and gini index in certain cases
 G-statistic: has a close approximation to χ2 distribution
 MDL (Minimal Description Length) principle (i.e., the simplest solution is
preferred):
 The best tree as the one that requires the fewest # of bits to both (1)
encode the tree, and (2) encode the exceptions to the tree
 Multivariate splits (partition based on multiple variable combinations)
 CART: finds multivariate splits based on a linear comb. of attrs.
 Which attribute selection measure is the best?
 Most give good results, none is significantly superior than others

15
Overfitting and Tree Pruning
 Overfitting: An induced tree may overfit the training data
 Too many branches, some may reflect anomalies due to
noise or outliers
 Poor accuracy for unseen samples
 Two approaches to avoid overfitting
 Prepruning: Halt tree construction early ̵ do not split a node
if this would result in the goodness measure falling below a
threshold
 Difficult to choose an appropriate threshold
 Postpruning: Remove branches from a “fully grown” tree—
get a sequence of progressively pruned trees
 Use a set of data different from the training data to
decide which is the “best pruned tree”

16
Enhancements to Basic Decision Tree
Induction
 Allow for continuous-valued attributes
 Dynamically define new discrete-valued attributes that
partition the continuous attribute value into a discrete set of
intervals
 Handle missing attribute values
 Assign the most common value of the attribute
 Assign probability to each of the possible values
 Attribute construction
 Create new attributes based on existing ones that are
sparsely represented
 This reduces fragmentation, repetition, and replication

17
Classification in Large Databases
 Classification—a classical problem extensively studied by
statisticians and machine learning researchers
 Scalability: Classifying data sets with millions of examples and
hundreds of attributes with reasonable speed
 Why is decision tree induction popular?
 relatively faster learning speed (than other classification
methods)
 convertible to simple and easy to understand classification
rules
 can use SQL queries for accessing databases
 comparable classification accuracy with other methods
 RainForest (VLDB’98 — Gehrke, Ramakrishnan & Ganti)
 Builds an AVC-list (attribute, value, class label)

18
Bayesian Classification: Why?
 A statistical classifier: performs probabilistic prediction, i.e.,
predicts class membership probabilities
 Foundation: Based on Bayes’ Theorem.
 Performance: A simple Bayesian classifier, naïve Bayesian
classifier, has comparable performance with decision tree and
selected neural network classifiers
 Incremental: Each training example can incrementally
increase/decrease the probability that a hypothesis is correct —
prior knowledge can be combined with observed data
 Standard: Even when Bayesian methods are computationally
intractable, they can provide a standard of optimal decision
making against which other methods can be measured

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Bayes’ Theorem: Basics
 Total probability Theorem:
 Bayes’ Theorem:
 Let X be a data sample (“evidence”): class label is unknown
 Let H be a hypothesis that X belongs to class C
 Classification is to determine P(H|X), (i.e., posteriori probability): the
probability that the hypothesis holds given the observed data sample X
 P(H) (prior probability): the initial probability
 E.g., X will buy computer, regardless of age, income, …
 P(X): probability that sample data is observed
 P(X|H) (likelihood): the probability of observing the sample X, given that
the hypothesis holds
 E.g., Given that X will buy computer, the prob. that X is 31..40,
medium income
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Prediction Based on Bayes’ Theorem
 Given training data X, posteriori probability of a hypothesis H,
P(H|X), follows the Bayes’ theorem
 Informally, this can be viewed as
posteriori = likelihood x prior/evidence
 Predicts X belongs to Ci iff the probability P(Ci|X) is the highest
among all the P(Ck|X) for all the k classes
 Practical difficulty: It requires initial knowledge of many
probabilities, involving significant computational cost
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Naïve Bayes Classifier
 A simplified assumption: attributes are conditionally
independent (i.e., no dependence relation between
attributes):
 This greatly reduces the computation cost: Only counts the
class distribution
 If Ak is categorical, P(xk|Ci) is the # of tuples in Ci having value xk
for Ak divided by |Ci, D| (# of tuples of Ci in D)
 If Ak is continous-valued, P(xk|Ci) is usually computed based on
Gaussian distribution with a mean μ and standard deviation σ
and P(xk|Ci) is
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22
Naïve Bayes Classifier: Training Dataset
Class:
C1:buys_computer = ‘yes’
C2:buys_computer = ‘no’
Data to be classified:
X = (age <=30,
Income = medium,
Student = yes
Credit_rating = Fair)
age income student
credit_rating
buys_compu

23
Naïve Bayes Classifier: An Example
 P(Ci): P(buys_computer = “yes”) = 9/14 = 0.643
P(buys_computer = “no”) = 5/14= 0.357
 Compute P(X|Ci) for each class
P(age = “<=30” | buys_computer = “yes”) = 2/9 = 0.222
P(age = “<= 30” | buys_computer = “no”) = 3/5 = 0.6
P(income = “medium” | buys_computer = “yes”) = 4/9 = 0.444
P(income = “medium” | buys_computer = “no”) = 2/5 = 0.4
P(student = “yes” | buys_computer = “yes) = 6/9 = 0.667
P(student = “yes” | buys_computer = “no”) = 1/5 = 0.2
P(credit_rating = “fair” | buys_computer = “yes”) = 6/9 = 0.667
P(credit_rating = “fair” | buys_computer = “no”) = 2/5 = 0.4
 X = (age <= 30 , income = medium, student = yes, credit_rating = fair)
P(X|Ci) : P(X|buys_computer = “yes”) = 0.222 x 0.444 x 0.667 x 0.667 = 0.044
P(X|buys_computer = “no”) = 0.6 x 0.4 x 0.2 x 0.4 = 0.019
P(X|Ci)*P(Ci) : P(X|buys_computer = “yes”) * P(buys_computer = “yes”) = 0.028
P(X|buys_computer = “no”) * P(buys_computer = “no”) = 0.007
Therefore, X belongs to class (“buys_computer = yes”)
age income student
credit_rating
buys_comp

24
Avoiding the Zero-Probability
Problem
 Naïve Bayesian prediction requires each conditional prob. be
non-zero. Otherwise, the predicted prob. will be zero
 Ex. Suppose a dataset with 1000 tuples, income=low (0),
income= medium (990), and income = high (10)
 Use Laplacian correction (or Laplacian estimator)
 Adding 1 to each case
Prob(income = low) = 1/1003
Prob(income = medium) = 991/1003
Prob(income = high) = 11/1003
 The “corrected” prob. estimates are close to their
“uncorrected” counterparts
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25
Naïve Bayes Classifier: Comments
 Advantages
 Easy to implement
 Good results obtained in most of the cases
 Disadvantages
 Assumption: class conditional independence, therefore loss
of accuracy
 Practically, dependencies exist among variables
 E.g., hospitals: patients: Profile: age, family history, etc.
Symptoms: fever, cough etc., Disease: lung cancer,
diabetes, etc.
 Dependencies among these cannot be modeled by Naïve
Bayes Classifier
 How to deal with these dependencies? Bayesian Belief Networks

26
Naïve Bayes Classifier: Types
 Gaussian Naive Bayes classifier
 In Gaussian Naive Bayes, continuous values associated with each feature
are assumed to be distributed according to a Gaussian distribution. A
Gaussian distribution is also called Normal distribution.
 Multinomial Naive Bayes
 Feature vectors represent the frequencies with which certain events have
been generated by a multinomial distribution. This is the event model
typically used for document classification.
 Bernoulli Naive Bayes
 In the multivariate Bernoulli event model, features are independent
booleans (binary variables) describing inputs. Like the multinomial model,
this model is popular for document classification tasks, where binary term
occurrence(i.e. a word occurs in a document or not) features are used
rather than term frequencies(i.e. frequency of a word in the document).

Summary (I)
 Classification is a form of data analysis that extracts models
describing important data classes.
 Effective and scalable methods have been developed for decision
tree induction, Naive Bayesian classification, rule-based
classification, and many other classification methods.
 Evaluation metrics include: accuracy, sensitivity, specificity,
precision, recall, F measure, and Fß measure.
 Stratified k-fold cross-validation is recommended for accuracy
estimation. Bagging and boosting can be used to increase overall
accuracy by learning and combining a series of individual models.
27

Summary (II)
 Significance tests and ROC curves are useful for model selection.
 There have been numerous comparisons of the different
classification methods; the matter remains a research topic
 No single method has been found to be superior over all others
for all data sets
 Issues such as accuracy, training time, robustness, scalability,
and interpretability must be considered and can involve trade-
offs, further complicating the quest for an overall superior
method
28

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