Successive iteration method for reconstruction of missing data

International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-
6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 2, March – April (2013), © IAEME
437
SUCCESSIVE ITERATION METHOD FOR RECONSTRUCTION OF
MISSING DATA
T.Jayalakshmi
CMS College of Science and Commerce, Bharathiar University, India
ABSTRACT
The information age has made a large amount of data available for medical
information processing. Occasional failures lead to missing data. The missing data may make
it difficult to apply analytical models. Data imputation techniques help us fill the missing data
with a reasonable prediction of what the missing values would have been. The implemented
system creates successive iteration method and various other missing value techniques. The
system achieves better performance than other methods.
Keywords: Artificial Neural Networks; Back Propagation Method; Diabetes Mellitus;
Missing Value Analysis, Pre Processing Methods; Successive Iteration Method.
INTRODUCTION
ANN is a type of massively parallel computing architecture based on a brain like
behaviour. They work in a similar way as human brain is functioning. The neuron or nerve
cell is the basic building block of the brain. Neurons are connected in various ways to form
biological neural networks. They process information in the brain, and communicate
information from different parts of the body to the brain. In total, the human brain has 1014
to
1015
neurons [11]. Neurons receives inputs process them by a simple connections and
threshold operations and outputs a result. Neural networks are sophisticated modeling
techniques capable of modeling extremely complex functions. They are inspired by biological
models of neurological systems and is an established machine learning model with robust
learning properties and simple deployment. Nowadays, they are being successfully applied
across a wide range of problem domains, in areas like finance, medicine, engineering, pattern
recognition and image processing. Anywhere, that there are problem of prediction or
classification neural networks are being introduced.
The principle advantage of neural network is to generalize, adapting to signal
distortion and noise without loss of robustness. The back propagation algorithm is a very
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ISSN 0976 – 6367(Print)
ISSN 0976 – 6375(Online)
Volume 4, Issue 2, March – April (2013), pp. 437-447
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popular training algorithm in neural network research. Previous studies show that the
architecture of network can have significant effect on its performance. The performance of
the network also depends on the data given to the system. Real time processing applications
that are highly dependent on data often suffer from the problem of missing input variables.
Data incompleteness and estimation are important problems that have received relatively
little attention in the medical informatics research community. Most of the real world data are
seldom complete [20]. The problem of missing data poses difficulty in the analysis and
decision-making process [8]. Decision-making is highly depending on these data, requiring
methods of estimation that are accurate and efficient. Neural networks cannot interpret
missing values; it requires complete set of data for improving the performance [4]. There are
many situations where input feature vectors are incomplete and methods to tackle the
problem have been studied for a long time. A commonly used procedure is to replace each
missing variable value with an estimated value or imputation obtained from the non-missing
values of other variables in the same unit. Some intelligent techniques are needed to replace
the missing data.
Diabetes is a disease that is characterized by an elevated blood glucose level. This can
be caused by a reduction of the production of insulin by the pancreas (Type I diabetes) or by
the insulin being less effective at moving glucose out of the blood stream and into cells that
need it (Type II diabetes). The blood glucose level that is elevated for a long period can result
in metabolic complications such as kidney failure, blindness, and an increased chance of
heart attacks. To prevent or postpone such complications strict control over the diabetic blood
glucose level is needed [7]. The aim of this study is to classify the Type II diabetes of Pima
Indian Diabetes data set. It is the most challenging problem in machine learning because of
the high noise level [15][16].To remove the noise and achieve the efficient classification two
important techniques were introduced: missing value analysis techniques and preprocessing
techniques.
This paper presents an alternative to the usual iterative method for determining the
approximate value. The method developed is based on the standard numerical analysis
technique of successive approximations or iterations. Reconstruction of missing values may
shift input patterns, and the network may have to settle on a complicated solution to satisfy
all reconstructed patterns. Successive approximations give correct results comparing to other
methods. This paper organized as follows: Section II briefs about the background study,
Section III describes about Artificial neural networks, Section IV deals about diabetes
mellitus, Section V gives the methodology of the proposed system, and Section VI concludes
the paper.
BACKGROUND STUDY
Siti Farhanah Bt Jaafar and Darmawati Mohd Ali [26] proposes a network with eight inputs
and four inputs and the results obtained are compared in terms of error. The highest
performance is obtained when the network consists of eight inputs with three hidden layers
with 15, 14, 14, 1 neurons respectively. Amit Gupta and Monica Lam [2] investigate the
generalization power of a modified back propagation training algorithm such as weight
decay. The effect of the weight decay method with missing values can be applied for different
data sets such as EPS data set, ECHO data set, IRIS data set etc. The missing values can be
reconstructed using standard back propagation, iterative multiple regression, replace by
average and replace by zero. The weight decay method achieves significant improvement

439
over the standard back propagation method. Fulufhelo V.Nelwamondo, Shakir Mohamed and
Tshilidzi Marwala [8] discuss the expectation maximization algorithm and the auto
associative neural network and genetic algorithm combination. The results show that for
some variables EM algorithm is able to produce better accuracy while for the other variables
the neural network and GA system is better. The findings shows that the methods used are
highly problem dependent. Colleen M.Ennett, Monique Frize, C.Robin Walker [4]
investigates the impact of ANN performance when predicting neonatal mortality of
increasing the number of cases with missing values in the data sets. They proposes three
approaches such as delete all the values, Replace with mean, and Replace with normal to
predict Canadian neonatal Intensive care unit network’s database. The experimental results
were very promising. Junita Mohamad-saleh and Brain [ 12] proposes the Principle
Component Analysis method for elimination of correlated information in data. It has been
applied to the Electrical Capacitance Tomography data, which contains highly correlated due
to overlapping sensing areas. It can boost the generalization capability of a MLP, the PCA
technique also reduces the network training time due to the reduction in the input space
dimensionality. The findings suggest that PCA data processing method useful for improving
the performance of MLP systems, particularly in solving complex problems. Pasi Luukka
[21] presented a new approach using a similarity based Yu’s norms for the detection of
erythemato squamous diseases, diabetes, breast cancer, lung cancer and lymphography. The
domain contains records of patients with known diagnosis. The results are very promising
when using Yu’s norms for the diagnosis of patients taking into consideration the error rate.
The use of this preprocessing method enhanced the result over 30%. Stavros J.Perantonis and
Vassilis Virvilis [27] proposed a method for constructing salient features from a set of
features that are given as input to a feed forward neural network used for supervised learning.
The method exhibits some similarity to principle component analysis, but also takes into
account supervised character of the learning task. It provides a significant increase in
generalization ability with considerable reduction in the number of required input features.
ARTIFICIAL NEURAL NETWORKS
A Neural Network is a massively parallel distributed processor made up of simple
processing units, which has a natural propensity for storing experiential knowledge and
making it available for use. It is very sophisticated modeling technique capable of modeling
extremely complex functions. ANNs attempt to create machines that work in a similar way to
the human brain by building them using components that behave like biological neurons.
However the operation of artificial neural networks and artificial neuron is far more
simplified that the operation of the human brain. The brain consists of millions of these
neurons, which may be specialized in some task or not. The behaviour of the brain inspired to
devise an artificial neuron called perceptron, which is the basis of all neural network models.
It resembles the brain in two respects a) Knowledge is acquired by the networks from the
environment through a learning process. b) Interneuron connection strengths, known as
synaptic weights, are used to store the acquired knowledge. Neural networks have advantages
over classical statistical approaches especially when the training set size is small compared
with the dimensionality of the problem to be solved and the underlying data distribution is
unknown. Learning is essential to most of the neural network models. Learning can be
supervised, when the network is provided with the correct answer for the output during
training, or unsupervised, when no external teacher is present. E is the error calculated from

440
the actual output (d) to the calculated output (o). The goal of the neural network learning is to
iteratively adjust weights, in order to globally minimize a measure of the difference between
the actual output of the network and the desired output as specified by the teacher.
DIABETES MELLITUS
Diabetes mellitus is the most common endocrine disease. The disease is characterized
by metabolic abnormalities and by long-term complications involving the eyes, kidneys,
nerves, and blood vessels. The diagnosis of symptomatic diabetes is not difficult. When a
patient presents with signs and symptoms attributable to an osmotic diuresis and is found to
have hyperglycemia essentially all physicians agree that diabetes is present. The two major
types of diabetes are Type I diabetes and Type II diabetes. Type I diabetes usually diagnosed
in children and young adults, and was previously known as juvenile diabetes [22] [26]. Type
I diabetes mellitus (IDDM) patients do not produce insulin due to the destruction of the beta
cells of the pancreas. Therefore, therapy consists of the exogenous administration of insulin.
Type II diabetes is the most common form of diabetes. Type II diabetes mellitus (NIDDM)
patients do produce insulin endogenously but the effect and secretion of this insulin are
reduced compared to healthy subjects [6]. Currently cure does not exist for the diabetes, then
only option is to take care of the health of people affected, maintained their glucose levels in
the blood to the nearest possible normal values [9].
METHODOLOGY
The information age has made a large amount of data available for medical
information processing. Occasional failures lead to missing data. The missing data may make
it difficult to apply analytical models. Data imputation techniques help us fill the missing data
with a reasonable prediction of what the missing values would have been. The implemented
system compares various missing value techniques.
5.1 CLASSIFICATION DATA
The problem that has been chosen for this research is to classify the Type II diabetic
data using Levenberg Marquardt back propagation algorithm. To investigate the performance
of the proposed neural-based method, the classifier was applied to PIMA INDIAN
DIABETES dataset and has been collected from UCI machine learning repository [3]. The
data set is a two-class problem either positive or negative for diabetes disease. The data set is
different to classify because of the high noise level. It contains 768 data samples. Each
sample consists of personal data and the results of medical examination. The individual
attributes are
• Number of times pregnant
• Plasma glucose concentration
• Diastolic blood pressure(mmHg)
• Triceps skin fold thickness(mm)
• 2-hour serum insulin(mu U/ms)
• Body mass index(weight in kg/(height in m)) 2
• Diabetes pedigrees function
• Age(years)

441
The above dataset 268 patients are having diabetes, which can be interpreted as “1” and the
remaining patients are not having diabetes and can be interpreted as “0”. The network
topology used for this study is 8-8-8-1. i.e. one input layer, two hidden layers and one output
layer with eight input nodes, eight hidden nodes and one output node.
5.2 NETWORK ARCHITECTURE
Back propagation algorithm is the most commonly used algorithm and it is the simple
feed forward artificial neural networks. The algorithm adjusts network weights by error
propagation from the output to the input. During the training the network minimizes the error
by estimating the weights. The minimization procedure can be performed using the gradient-
descent approaches, in which the set of weight vectors consisting of weights is adjusted by
the learning parameters. The network parameters such as learning rate, momentum constant,
training error and number of epochs can be considered as 0.9, 0.9, 1e-008 and 100
respectively. Before training the weights are initialized to random values. The reason to
initialize weights with small values is to prevent saturation. To evaluate the performance of
the network the entire sample was randomly divided into training and test sample. The model
is tested using the standard rule of 80/20, where 80% of the samples are used for training and
20% is used for testing. In this classification method, training process is considered to be
successful when the MSE reaches the value 1e-008. On the other hand the training process
fails to converge when it reaches the maximum training time before reaching the desired
MSE. The training time of an algorithm is defined as the number of epochs required to meet
the stopping criterion.
5.3 MISSING DATA ANALYSIS
The problem of missing data poses difficulty in the analysis and decision making
processes. Decision making is highly depending on these data, requiring methods of
estimation that are accurate and efficient. Back propagation neural networks have been
applied for classification problems in real world situations. A drawback of this type of neural
network is that it requires a complete set of input data, and real world data is seldom
complete. The problem of databases containing missing values is a common one in the
medical environment. ANNs cannot interpret missing values, and when a database is highly
skewed, ANNs have difficulty in identifying the factors leading to a rare outcome. Imputation
is the substitution of some value for a missing data point or a missing component of a data
point. Once all missing values have been imputed, the dataset can then be analyzed using
standard techniques for complete data. The analysis should ideally take into account that
there is a greater degree of uncertainty than if the imputed values had actually been observed,
however, and this generally requires some modification of the standard complete-data
analysis methods.
5.4 METHODS
Missing information in data sets is more than a common scenario. There are different
methods to perform these imputations depending on the type of variable with missing data
and on the type of auxiliary variables. Here the imputation of categorical variables from other
numerical and categorical variables is studied. This paper presents an alternative to the usual
method for determining the approximate value. It is an alternative to the usual iterative
method for determining the approximate value. Iterative algorithms usually used when
explicit formulae are unavailable. The idea is that a repetition of simple calculations will

442
result in a sequence of approximate values for the quantity of interest. The method developed
is based on the standard numerical analysis technique of successive approximations or
iterations. Successive approximations give correct results comparing to other methods. The
mean of the same attribute is repeatedly calculated until it approximates the value. The
approximated value is replaced with the missing column.
a) Omit the Values: The easiest way to deal with missing values is simply delete all the
cases with missing values for the variable under consideration. This technique however may
lead to the loss of potentially valuable information about patients whose values are missing.
b) Replace with Mean: The second approach is to replace all missing values with the mean.
The method of replacing by average is to replace all missing values of an attribute by the
average of all available values of the same attribute in the training set. Replacing the missing
values with the means might bias the databases towards the sicker ones.
c) Replace with Zero: The third technique is to replace all the missing values with zeros.
The method of replacing by zero is simply to replace all missing values by zero. Replacing
missing values by zero in this study has the same effect of replacing missing values by the
smallest value of an attribute since data have been converted to be between zero and one. If
the values are important for clinical management the assessment of missing values leads to
poor classification.
d) Replace with K-nearest neighbor: The fourth technique K-nearest neighbor method
replaces missing values in data with the corresponding value from the nearest-neighbor
column. The nearest-neighbor column is the closest column in Euclidean distance. If the
corresponding value from the nearest-neighbor column is also contains missing value the next
nearest column is used.
e) Replace with Successive Iteration Method: The technique presented in this paper is to
replace the missing data with successive iteration method.
5.4.1 ALGORITHM
Step 1: Find the missing element in the data set.
Step 2: Calculate the mean of the attribute
Step 3: Substitute the mean with missing attributes
Step4: Find the new mean of the attribute
Step 5: Compare the new mean with the existing mean
Step 6: If both are same replace the mean with missing column attribute
Step 7: Otherwise repeat the steps 3-6 until the mean converges.
5.5 PREPROCESSING OF INPUT DATA
Neural network training could be made more efficient by performing certain
preprocessing steps on the network inputs and targets. Network input processing functions
transforms inputs into better form for the network use. The normalization process for the raw
inputs has great effect on preparing the data to be suitable for the training. Without this
normalization, training the neural networks would have been very slow. There are many
types of data normalization. It can be used to scale the data in the same range of values for
each input feature in order to minimize bias within the neural network for one feature to
another. Data normalization can also speed up training time by starting the training process
for each feature within the same scale. It is especially useful for modeling application where

443
the inputs are generally on widely different scales. Principle Component Analysis is a very
popular normalization method. Principal Component’s normalization is based on the premise
that the salient information in a given set of features lies in those features that have the largest
variance. This means that for a given set of data, the features that exhibit the most variance
are the most descriptive for determining differences between sets of data. This is
accomplished by using eigenvector analysis on either the covariance matrix or correlation
matrix for a set of data.
5.6 EXPERIMENTAL RESULTS
The system has been implemented to study the impact of pre-processing and missing
value techniques. The simulations have been carried out using MATLAB. Various networks
were developed and tested with random initial weights. The network is trained ten times and
the performance goal is achieved at different epochs.
Figure. 1. SIT Method without pre-processing
Figure. 2. SIT Method with pre-processing
Figure.3. Accuracy (without pre-processing)

444
Figure.4. Accuracy (With pre-processing)
TABLE I. IMPACT OF MISSING VALUES WITHOUT PRE-PROCESSING
Accuracy
62
64
66
68
70
72
74
76
Omit the
Values
Replace with
Zero
Replace with
Mean
Replace with
KNN
Replace with
SIT
Method
Accuracy
Performance
0
20
40
60
80
100
120
Omit the
Values
Replace with
Zero
Replace with
Mean
Replace with
KNN
Replace with
SIT
Method
Epochs
Accuracy
Epochs
Performance 1e-009
Method Accuracy Epochs
Performance
1e-009
Omit the Values 97.1 24 5.76
Replace with Zero 99 15 5.11
Replace with Mean 99.2 14 6.48
Replace with KNN 99 35 8.33
Replace with SIT 99.5 14 5.88

445
TABLE II. IMPACT OF MISSING VALUES WITH PRE-PROCESSING
The impact of the missing values can be assessed by taking the average of ten runs and
measured in terms of classification accuracy (Table.1) and training time (Table.2). It shows
that the accuracy was improved when replace with successive iteration method in
combination of PCA pre-processing method.
6 CONCLUSION
This paper demonstrates the impact of missing value technique and pre-processing
technique. It proves that some combination of missing values and pre-processing the
accuracy was tremendously improved. This shows that pre-processing and missing values
play a major role in classification. In future this can be applied for different training methods
and networks
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Successive iteration method for reconstruction of missing data

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