Accepted Manuscript

A Fuzzy Based Feature Selection from Independent Component Subspace for Machine learning Classification of Microarray Data

Rabia Aziz, C.K. Verma, Namita Srivastava

PII: S2213-5960(16)30034-4

DOI: doi: 10.1016/j.gdata.2016.02.012

Reference: GDATA 489

To appear in:

Genomics Data

Received date: Revised date: Accepted date:

29 October 2015 8 January 2016 19 February 2016

Please cite this article as: Rabia Aziz, C.K. Verma, Namita Srivastava, A Fuzzy Based Feature Selection from Independent Component Subspace for Machine learning Classification of Microarray Data, Genomics Data (2016), doi: 10.1016/j.gdata.2016.02.012

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A Fuzzy Based Feature Selection from Independent Component Subspace for Machine learning Classification of

Microarray Data Rabia Aziz*, C.K. Verma, Namita Srivastava Department of Mathematics & Computer Application, Maulana Azad National Institute of Technology Bhopal-462003 (M.P.) INDIA

Abstract

Feature (gene) selection and classification of microarray data are the two most interesting machine learning challenges. In the present work two existing feature selection/extraction algorithms, namely Independent component analysis (ICA) and Fuzzy backward feature elimination (FBFE) are used which is a new combination of selection/extraction. The main objective of this paper is to select the independent components of the DNA microarray data using FBFE to improve the performance of Support Vector Machine (SVM) and Naïve Bayes (NB) classifier, while making the computational expenses affordable. To show the validity of the proposed method, it is applied to reduce the number of genes for five DNA microarray datasets namely; Colon cancer, Acute leukemia, Prostate cancer, Lung cancer II, and High-grade Glioma. Now these datasets are then classified using SVM and NB classifier. Experimental results on these five microarray datasets demonstrate that gene selected by proposed approach, effectively improve the performance of SVM and NB classifiers in terms of classification accuracy. We compare our proposed method with principal component analysis (PCA) as an standard extraction algorithm and find that the proposed method can obtain better classification accuracy, using SVM and NB classifier with a smaller number of selected genes than the PCA. The curve between the average error rate and number of genes with each dataset represents the selection of required number of genes for the highest accuracy with our proposed method for both the classifiers. ROC shows best subset of genes for both the classifier of different datasets with propose method.

Keywords: Fuzzy backward feature elimination (FBFE); Independent component analysis (ICA); Support vector machine (SVM); Naïve Bayes (NB); Classification.

1. Introduction

Gene expression analysis using microarrays has become an important part of biomedical and clinical research. Recent advancements in DNA microarray technology have enabled us to monitor and evaluate the expression levels of thousands of genes simultaneously, which allows a great deal of microarray data to be generated [1]. Microarray techniques have been successfully employed virtually in every aspect of biomedical research because they exhibit the

possibility to do massive tests on genome patterns [2]. Microarray gene expression data usually has a large number of dimensions and is permitted to evaluate each gene in a single environment in different types of tissues like various cancerous tissues [3]. Accordingly, microarray data analysis, which can supply useful data for cancer prediction and diagnosis, has also attracted many researchers from diverse areas. Progressively, the challenge is to translate such data to get a clear insight into biological processes and the mechanisms of human disease [4]. To aid such discoveries, mathematical and computational tools are required that are versatile enough to capture the underlying biology and simple enough to be applied efficiently on large datasets. Therefore, novel statistical methods must be introduced to analyze those large amounts of data generated from microarray experiments [5]. The process of microarray classification consists of two successive steps. The first step is to select a set of significant and relevant genes and the second step is to develop a classification model, which can produce accurate prediction for unseen data. One of the key goals of microarray data analysis is to distinguish the various categories of cancers. A true and accurate classification is essential for successful diagnosis and treatment of cancer. The enormous dimensionality of the DNA microarray data becomes a problem, when it is employed for cancer classification, as the sample size of DNA- microarray is far less than the gene size [6]. However, among the large number of genes, only a small fraction is effective for performing a classification task, so the choice of relevant genes is an important task in most microarray data studies that will give higher accuracy for sample classification (for example, to distinguish cancerous from normal tissues). This trouble can be alleviated by using machine learning with a gene selection problem. The goal of gene selection methods is to determine a small subset of informative genes that reduces processing time and provides higher classification accuracy [7]. There are a large number of methods, which have been developed and applied to do gene selection. A typical gene selection method has two constituents, an evaluation criterion and a searching scheme. As many evaluation criteria and searching schemes already exist, it is possible to develop many gene selection methods by just combining different evaluation criteria and searching schemes. Since, many of these combinations of evaluation criteria and searching schemes actually perform similarly, it is sufficient to compare the most commonly used combinations instead of all possible combinations [8]. The commonly used gene selection & extraction approaches are t-test, Relief-F, Information gain, SNR-test and Principal Component Analysis (PCA), Linear Discriminant Analysis, Independent component analysis (ICA). These methods are capable of selecting a smaller subset of genes for sample classification [9]. Recently, Independent component analysis (ICA) method has received growing attention as effective data-mining tools for microarray gene expression data. As a technique of higher-order statistical analysis, ICA is capable of extracting biologically relevant gene expression features of microarray data [10]. The success of the ICA method depends upon the appropriate choice of best gene subset from given ICA feature vector and choice of an appropriate classifier [11].

In this study, fuzzy backward feature elimination (FBFE) scheme was introduced, in which features were eliminated successively from ICA feature vector according to their influence on a SVM and NB based evaluation criterion. FBFE is a backward feature elimination method based on fuzzy entropy measure. Several machine learning techniques, such as Artificial neural networks (ANN), k-nearest neighbor (KNN), Support vector machine (SVM), Naïve Bayes (NB), Decision Tree, Random Forest and kernel-based classifiers, have been successfully applied to microarray data and also for other biological data analyses in recent years [4, 12]. From the study of Liwei Fan et al (2009) and Chun-Hou Zheng (2006), It was seen that NB and SVM were the best classifiers with ICA for microarray data, and feature subset selection from the ICA feature vector can significantly improve the performance of classifiers [3, 13].

Naïve Bayes (NB) classifier is a simple Bayesian network classifier, which is built upon the firm assumption that different attributes are independent of each other in the given course of instruction. There are two major challenges that may seriously affect the successful application of NB classifier to microarray data analysis. The first is the conditional independence assumption rooted in the classifier itself, which is hardly satisfied by the microarray data [14]. This limitation could be successfully resolved as the components extracted by the ICA are statistically independent therefore, gene extraction by ICA could effectively improve the performance of a NB classifier for microarray data. Second limitation is that, all the attributes have an influence on the classification; hence, the use of FBFE eliminates the inappropriate genes from ICA feature vector to improve the performance of a NB classifier during cross validation. It is therefore necessary to select genes to reduce the dimensionality of microarray data before applying a NB classifier [15]. On the other hand the SVM-based classifier is superior, as it is less sensitive to the curse of dimensionality and more robust than other non-SVM classifiers [16]. The biggest drawback of an SVM is that it cannot directly obtain the genes of importance. Thus, during the fitting of an SVM model, a careful gene selection has to be done first and then the selected genes should be used to obtain improved classification results. If genes are not appropriately chosen, there may be a large number of redundant variables in the model, severely affecting its performance [17].

In this paper, a Fuzzy backward feature elimination (FBFE) approach is used to eliminate the inappropriate genes from the independent components of the DNA microarray data for support vector machine (SVM) and Naïve Bayes (NB) classifiers. The proposed approach consists of mainly two steps. The original DNA microarray gene expression data are modeled by independent component analysis (ICA), and then the most discriminant features extracted by the ICA are selected by the Fuzzy feature selection technique, which will be introduced and discussed in detail in section 2. The next section explains the classification procedure of SVM and NB, followed by the details of used datasets and preprocessing step of datasets. In Section 5, the proposed method is compared and evaluated with PCA as a standard extraction methods on several microarray datasets. The experimental results on five microarray datasets, shows that the

proposed approach can, not only improve the average classification accuracy rates, but also reduce the variance in classification performance of SVM and NB. Discussions and conclusions are presented in section 6. 2. Proposed approach

2.1 Feature extraction by ICA

ICA is a projection method that linearly decomposes the dataset into components that have a desired property. ICA decomposes an input dataset into components such that each component is statistically as independent from the others as possible, which was proposed by Hyvarinen and has been proven successful in many applications [18]. ICA is an extension of PCA; PCA projects the data into a new space spanned by the principal components. In contrast to PCA, the goal of ICA is to find a linear representation of non-Gaussian data so that the components are statistically independent [19]. ICA provides a more biologically plausible model for gene expression data by assuming a non-Gaussian data distribution. ICA provides a data-driven method for exploring functional relationships and grouping genes into transcriptional modules.

In the simplest form of ICA, the expression levels of all genes are taken as n scalar random variables Xi, X2,... Xn, which are assumed to be linear combinations of m unknown independent components S1, S2,... Sm that is mutually statistically independent, and possess zero-mean. Let the expression levels Xjbe arranged into a vector X = (x1, x2, ..., xn)T which are modeled as linear combination of m random variable S = (s1, s2,... sm) T [20]:

xj = aj1s1 + aj2s2 + ... + ajmsm , for ^ J = 1

a11 . . a1m

(1) (2)

Where X is (n x m) matrix which denotes microarray gene expression data, with n genes and m samples, and

a .., (i =1,............, m) in X are some real ratio of intensities, represent the expression level of ith genes in the Jth sample,

and number of genes are much greater than that of the sample m i.e., n >> m. This is a basic ICA model of microarray gene expression data. It is assumed that the observed variables are independent components, these are latent variable, which cannot be directly observed and the mixing matrix A is also assumed to be unknown matrix. The random variable Xj is known and both the matrix S and A using X are to be estimated. In most cases, to simplify features selection, the number of features is always assumed to be equal to the number of observed variables, n = m. Then, the mixing matrix A becomes an m x m square matrix and can invert the mixing matrix as:

U = S = A~1X = WX (3)

Then ICA can be applied to find a matrix Wthat provides the transformation U = u1,u2,.........um = WX of the observed

matrix X under which, the transformed random variables u1, u2,.........um called the independent components are as

independent as possible. Theoretical framework of ICA algorithms of microarray gene expression data is shown in figure 1, as previously demonstrated by Wei Kong et al [21].

Figure 1

A fixed point algorithm is a computationally highly efficient method for performing the estimation of ICA for microarray data [22]. It is based on a fixed-point iteration scheme that has been found in independent experiments to be 10-100 times faster than conventional gradient descent methods for ICA. In the fixed point algorithm of ICA (FastICA), maximizing negentropy is used as the contrast function since negentropy is an excellent measure of non-Gaussianity and is approximated by

J(u) = H (ug ) - H(u) (4)

where uG is a Gaussian random vector of the same covariance matrix as vector u, H is marginal entropy, which is defined as H(ui) = —Jp(si )losp(si )dsi of the variable ut andp (.) is a probabilistic density function. Mutual information

I, is known as natural measure independence of random variables, it is widely used as the criterion in ICA algorithm and can be measured by

I = J (u) — ^ J (u,-) (5)

The independent components are determined, when mutual information I is minimized. From equation (5), it is clearly shown that minimizing the mutual information I is equivalent to maximizing the negentropy J (u). To estimate the

negentropy of ui = w x , an approximation to identify independent components one by one is designed as follows:

Jg (w) = [E{G(wTx)} — E{G(v)}]2 (6)

where, G can be practically any non-quadratic function, E (.) denotes the expectation, and v is a Gaussian variable of zero

mean and unit variance [23].

2.2 Feature selection by FBFE technique

Fuzzy feature selection approach is used to select the best gene subset from the ICA feature vector for good separability of the classification task. A central issue associated with ICA is, it generally extracts a number of components, which are equal to the observational variables m for which again 2m gene subsets exist (Zheng, et al. 2008).

The evaluation of all possible gene subsets leads to computational problem for large values of m. To solve this problem of identifying the most relevant feature subsets FBFE technique is applied.

Fuzzy feature selection is based on a fuzzy entropy measure. Since the fuzzy entropy is able to discriminate pattern distribution better, it is employed to evaluate the separability of each feature. Intuitively, the lower the fuzzy entropy of a feature, the higher is the feature's discriminating ability. Pasi Luukka (2011) suggested that corresponding to Shannon probabilistic entropy, the measure of fuzzy entropy should be [24].

Hi(A) = - X (pA(Xj)log^A(x;)+(1 ~^A(xj))log(1 -vA(xj))) (7)

where HA(Xj) are the fuzzy values. This fuzzy entropy measure is considered to be a measure of fuzziness, and it

evaluates global deviations from the type of ordinary sets, i.e. any crisp set A0 lead to h (A0) = 0. Note that the fuzzy set A withma(xj) = 0.5 plays the role of the maximum element of the ordering defined by H. Newer fuzzy entropy

measures were introduced by Parkash et al. [25] where fuzzy entropies were defined as:

n Tin A (Xj) t(1 -K^A (Xj))

(sir 1

H2 (A: w) = X w- (sin-— + sin-j--1) (8)

•'A 2 2

n (xj) T(1-TflA (x'))

H3 (A : w) = X w - (cos-— + cos-j--1) (9)

j = 1 j 2 2

These fuzzy entropy measures were used in the feature selection process. The main idea is, first to create the ideal vectors V = (Vi(fi )>■■■> v'(ft)) that represents the class i as well as possible. This vector can be user defined or calculated from some sample set Xi of vectors x = (xf), . . . , x (f)) which are known to belong to class C. Here the generalized mean is used to create these class ideal vectors. Then the similarities S (x, V), between the sample x and the ideal vectors Vi are calculated. In calculating the similarity of the sample vectors and ideal vectors, j similarities are obtained, where j is the number of features. Then those similarities are collected into one similarity matrix. At this step, using the equation (7) entropy is calculated to evaluate the relevance of the features. Low entropy values are obtained if similarity values are high and if similarity values are close to 0.5, high entropy values are obtained. Using this underlying idea, the fuzzy entropy values can be calculated for features by using similarity values between the ideal vectors and sample vectors which are to be classified [26]. After the fuzzy entropy of each feature has been determined, the features can be selected by forward selection or backward elimination. The forward selection method is to select the relevant features beginning with an empty set and iteratively add features until the termination criterion is met. In contrast, the backward elimination method starts with the full feature set and removes features until the termination criterion is met [27]. In this paper a backward elimination method is used to pick the relevant features.

2.3 Performance evaluation method (LOOCV)

The Leave-One-Out Cross-Validation (LOOCV), performance is applied to characterize the behaviour of both the base classifiers. Two typical cross-validation methods (namely k-fold cross-validation and leave-one-out validation) have been widely used in microarray data classification evaluation. Comparing to the k-fold cross-validation method, the LOOCV method is more applicable due to the small sample size of microarray data [4, 9, 11, 28]. In LOOCV method of cross validation the number of partitions of a data set is equal to the number of sample size (m). Each test set consists of a different singleton set and each training set consists of all (m -1) cases not in the corresponding test set. Given a dataset containing m samples, (m -1) samples are used to construct a classifier and then apply the remaining one data sample to test this classifier. By repeating this process of successively using each data samples (x) as the testing data sample, totally m prediction ei = c(xi) (i = 1-m) are obtained. The performance of the classifier is then measured by the average misclassification rate:

Er = — ^S(ei > yi X i=1

Where yi, is the true class label, for instance xi, and

xt ^ I0 if x = y

S( x, y) ...

II i) x * y

2.4 SVM classifier

The support vector machine (SVM) is a popular algorithm for solving, pattern recognition, regression and density estimation problems, and perform better than most of the machine learning algorithms introduced by Vapnik and Co-workers [29-31]. The SVM is a linear classifier that maximizes the margin between the separating hyperplane and the training data points. In case of linearly separable data, the goal of training phase of SVM is to find the linear function[32]:

f (x) = WTX + b (10)

For the given training data set that consists of n samples, (x, y) for i = 1, 2,..., n, xt £ Rd represents input vectors andyt denotes the class label of the ith sample. In the binary SVM the class labels yt is either 1 or -1 i.e. yi £ (-1, +1), equation (10) is the border for two different data classes and divides the space into two classes according to the condition: WTX + b > 0 , WTX + b < 0 , Where W £ Rn is a normal vector, the bias b is a scalar; the separating plane is defined

by WT X + b = 0 , and the distance between the two parallel hyperplane is equal to . This quantity is termed

IIW112

as the classification margin as shown in figure 2. For maximizing the classification margin the SVM requires the solution of the following quadratic optimization problem [33, 34]:

min imize 1|| W||2 (11)

subjectto Yt(WTXi + b) > 1

By introducing Lagrange multipliers a (i = 1, 2,..., n) for the constraint, the primal problem becomes a task of finding the saddle point of Lagrange. Thus, the dual problem becomes:

L(a) = - - aj y y}- ( x. Xj ) (12)

i=1 ij n

ibjectto ~^aiyi = 0 i=1

By applying the Karush-Kuhn-Tucker (KKT) conditions, the following relationship holds a, [y - (W x + b) -1 ] If a > 0, the corresponding data points are called support vectors (SVs). Hence, the optimal solution for the normal vector is given

by w * = ^a-y■ x■ Here N is the number of SVs. By choosing any SVs (xk, yk), we can obtain b*=yk-W* xk

After (W*, b*) is determined, the discrimination function can be given by

f( x) = sgn

S aiyi(xi.xj) +b * [f = - j

Where sign (.) is the sign function.

In case of nonlinearly separable data, SVM has to map the data from the input space into a higher-dimensional feature space, where the classes can then be separated by a hyperplane. The function that performs this mapping is called a kernel function. In SVM the following four basic Kernel functions are used [35]:

1. Linear: K(X,X ¡) = xjX ,■

i J * J

2. Polynomial K(Xt,Xj) = (yXTi,Xj + r)d, y> 0

3. Radialbasisfunction(RBF): K(X* , X j ) = exp(-^|Xi - Xj 11)2, y> 0

4. Sigmoid: K(Xt,Xj ):tanh (yX,T,Xj + r) Where r, d and y is a kernel parameter.

For nonlinearly separable data, SVM requires the solution of the following optimization problem:

1 II tI|2

min imize WT|| + C Y.t=" £ (14)

subjectto: Yt (WT Xi + b) > 1

Where £ > 0 are slack variables that allow the elements of the training data set to be at the margin or to be misclassified [36].More detailed information on SVM can be found elsewhere [32, 37].

2.5 Naïve Bayes classifier

Naïve Bayes is one of the most efficient and effective inductive learning algorithms for machine learning and data mining, based on applying Bayes theorem with strong independence assumption [38-40]. After feature selection, Naïve Bayes classifier is built, which is used to classify a new test sample with features (gene) values Ej, E2,. . ., En. Bayesian network classifier computes the posterior probability that the sample belongs to class H by using the Bayes theorem for multiple evidences as follows [1, 41, 42]:

P(Ei,E2,E3,...,En | H)xP(H)

P(H| E',E2,E3,..,En)--^-pé;:hE^::Èy-^ (15)

If the assumption of class-conditional independence among attributes is imposed, the following Naïve Bayes classifier can be obtained[15]:

P(H | E^ES ,..., En ) - ^ H ) X P(E2I H ) X... P(Enl H ) X P(H ) (i6)

P(Ej,E2,E3,..., En )

Since P(Ej,E2,E3,...,En) is a common factor for a certain sample, it can be ignored in the classification process. In addition, since the attribute variables are continuous in microarray data analysis, the probability density value f ( Ei | H) can be used to replace the probability value P( Ei | H). The class-conditional probability density f ( . | H) for each attribute and the prior P( H)can be obtained from the learning process. For the estimation of f ( ^H) the nonparametric kernel density estimation method is used [13, 40, 43]. As a result, the general Bayesian classifier given by Eq. (17) can be simplified as the Naïve Bayes classifier given by Eq. (19). Figure 3 shows the simplified form of a Bayesian classifier as the Naïve Bayes classifier [44].

H' - argmax P(Hf (Et | H) (17)

H em A A

Figure 3

4. Experiential setup

To evaluate the performance of the proposed feature selection approach for SVM and NB classifier five publicly available microarray data sets, i.e. Colon cancer [45], Acute leukemia [46], Prostate cancer [47], Lung cancer-II [48], and High-grade Glioma data [49] are taken. These datasets have been widely used to benchmark for the performance of gene selection methods in bioinformatics field. These datasets is downloaded from Kent ridge an online

repository of high-dimensional biomedical data sets, (http://datam.i2r.astar.edu.sg/datasets/krbd/index.html). Table 1 shows the five datasets with their properties. Table 1

These datasets are preprocessed by setting thresholds and log-transformation on the original data. After preprocessing the data, it is divided into training and test set, further independent component analysis is performed to reduce the dimensionality of train data. For ICA, the FastICA algorithm software package for Matlab (R2010a) is applied it can be obtained from [53]. Then fuzzy feature selection technique is used for finding a small number of genes in independent component feature vectors. Codes for fuzzy feature selection are freely available on internet [54].

In this study, we tested the performance of the proposed fuzzy ICA algorithm by comparing it with most well-known standard extraction algorithms principal component analysis (PCA) [50].We compared the performance of each gene selection approach based on two parameters: the classification accuracy and the number of predicted genes that have been used for cancer classification. Classification accuracy is the overall precision of the classifier and is calculated as the sum of correct cancer classifications divided by the total number of classifications:

Classification.Accuracy= * 100

where N is the total number of the instances in the initial microarray dataset and CC refers to correct classified instances. From early stage of the SVM, most of the researchers have used the linear, polynomial and RBF kernels for classification problems. From these kernels polynomial and RBF are the nonlinear kernel and cancer classification using microarray dataset is a nonlinear classification task [51, 52]. Nahar et al. (2007) observed from their experiment out of nine microarray datasets that the polynomial kernel is a first choice for microarray classification. Therefore, we used polynomial kernel for SVM classifier with parameter gamma = 1, d = 3 and value of 1 is used for the complexity constant parameter C and the random number of seed parameter W. In addition, we apply leave-one-out cross-validation (LOOCV) in order to evaluate the performance of our proposed algorithm with SVM and NB classifier. We implement SVM, NB using the MATLAB software. Furthermore, in order to make experiments more statistically valid, we conduct each experiment 30 times on each dataset. In addition, average results and variance of the classification accuracies of the 30 independent runs are calculated in order to evaluate the performance of our proposed algorithm.

5. Experimental result

To check the performance of the proposed approach with SVM and NB classifier, the above mentioned combination has been applied on the five DNA microarray gene expression datasets. Since all data samples in the five

datasets have already been assigned to a training set or test set. The training dataset is used to do gene selection and then built the model for classification of the test dataset to evaluate the performances of alternative classifiers. To show the efficiency and feasibility of our proposed method, the results of the other three gene selection methods for the same classifier are also listed in Table 2 to 6 for comparison. In method 1, the microarray data are classified by SVM directly with all features. In the Method 2, all the features are extracted by principle component analysis for SVM classification and the same is applied for method 3 except using ICA for feature extraction. Method 4 is similar to our proposed method where PCA is used with FBFE for SVM classification and in method 5 ICA with FBFE. The classification for pure Naive Bayes classifier was not included due to its extremely time-consuming computations. In Method 1 of NB classification PCA was used for feature extraction, in second ICA was used with NB. In method 3 and 4 PCA and ICA was used with FBFE for NB classification respectively.

Table 2 Table 3 Table 4 Table 5 Table 6

It can be seen from Table 2-6 that both FBFE+PCA and FBFE+ICA perform better than PCA and ICA in microarray data analysis, which demonstrates the effectiveness of the proposed approach. As for the comparison between the former two classification rules, FBFE+ICA perform obviously better than FBFE+PCA in terms of classification accuracy for both the classifier. It is clear that the classification accuracy of classifiers with our proposed method compared to other three gene selection methods with same classifiers is more accurate, feasible and reduces the variation of classification performance. Therefore, the proposed approach improves the classification performance of both the classifiers for microarray data. From the accuracy table of different dataset 2-6, the performance of the proposed method for the High-grade Glioma data, in contrast to other 4 used datasets is low, because there is no method, which could be applied universally to all the datasets to classify with maximum accuracy, since the properties of every data sets are different.

Since, a small number of features are not enough for classification, while a large number of features may add noise and cause over fitting, fuzzy based backward elimination method is used for removing inappropriate genes from the independent component feature vector and the termination criterion in our method is based on the classification accuracy rate of the classifier. Since features with higher fuzzy entropy are less relevant to our classification goal, eliminate the feature which has the highest fuzzy entropy. If the classification rate does not decrease, then the above step is repeated

until all "inappropriate" features are removed. Finally, the features remained were used for classification and then mean classification accuracies and variances were computed. In order to study the behavior of a proposed feature selection approach, it is applied to the Colon, Leukemia, Prostate, High-grade Glioma and Lung cancer II data set for SVM and NB classification, a graph is plotted between the number of features and classification accuracy rates. Figure 4-8 shows the variation of the number of selected genes V/s classification accuracy, using SVM and NB classifier.

Figure 4 - 8

Colon Cancer dataset consist of 62 samples with 2000 (genes) features of two classes. Figure 4 shows the graph between the number of selected genes and the classification accuracy, using SVM and NB classifier for colon cancer data based on the proposed gene selection method. Here by reducing the gene, the mean classification accuracy enhances significantly. The classification accuracy with all 61 selected genes of training set was 79.19 %. The mean improvement in classification accuracy was verified by eliminating 5 genes, each time from training sets. Interestingly, the best mean accuracy with the proposed method was found 90.09 % for 30 selected features and 85.46 % for 25 selected genes with SVM and NB classifiers respectively. There is a sudden increase in the classification accuracy with the elimination of the genes from 61 to 30 for SVM classification, further reduction in the genes again decreases the classification accuracy. Moreover, as can be seen from figure 4, the results were improving almost all the time, when genes were reduced and finally best results were obtained, using only 30 and 25 genes from the training data set using SVM and NB classifier respectively. This also suggests a significant reduction in computational cost and simplifies the model a lot.

Acute leukemia dataset consists of 72 samples with 7129 genes of two classes. Figure 5 shows the results of classification accuracy with the number of selected genes for leukemia dataset. As shown in Table 3, with this data set using SVM and NB classifier with ICA feature vector, the highest mean accuracy obtained was 88.23 % and 86.21 %. When FBFE approach is used in independent component feature vector, one managed to get 94.2 % and 95.12 % mean classification accuracies for SVM and NB classifier respectively. Fuzzy backward feature elimination (FBFE) approach is used to eliminate the irrelevant and correlated genes from the independent components. The peak of the graphs shows that here, 35 genes for SVM and 30 genes for NB were used for best classification accuracy.

Figure 6 shows the graph for the classification accuracy of the prostate cancer dataset with a number of selected genes using FBFE and ICA approach with SVM and NB classifier. The peak of the graph shows the maximum classification accuracy of this dataset. Interestingly, for both SVM and NB classifier the selection of 50 genes gives highest mean classification accuracy. Classification accuracy of this dataset with SVM classifier is more as compared with the NB classifier with the same number of selected genes. Though the classification accuracy with ICA + SVM and

ICA + NB as shown in the table 4 was 80.45 % and 79.23 %, the mean classification accuracy for SVM and NB classifier is 88.12 % and 84.12 % respectively with the proposed approach. These results clearly show that the FBFE approach with ICA performs better than the other existing methods.

High-grade Glioma dataset consist of 50 samples with 12625 genes of two classes. From this data set 49 genes are extracted by FastICA from the training set. Figure 7 shows the classification accuracy graph of High-grade Glioma data by the elimination of the genes with FBFE, using SVM and NB classifier. From the figure 5 it is clear that, by eliminating 5 genes here for this data, there is a difference of 10 genes between the SVM and NB classification for the highest mean classification accuracy which is more as compared with the other selections. It can be seen from the graph that the highest mean accuracies for Glioma dataset was found with 25 and 35 (with the difference of 10 genes) selected genes for SVM and NB classification respectively. There is a gradual increase in the classification accuracy with the elimination of genes for both SVM and NB classification. The values of mean classification accuracy with the proposed method for SVM and NB classifiers are 79.21 % and 76.23 %, respectively, which is very low as compared to the accuracies of other datasets.

In lung cancer-II data set there were 181 samples with 12533 genes. Figure 8 clearly shows the difference between the classification accuracies of this dataset using SVM and NB classifier. It is clear from the accuracy graph that classification accuracy of NB is more as compared to the accuracy of the SVM classifier with our proposed method. A sudden increase in the mean classification accuracy is seen with the elimination of the genes using ICA and FBFE with SVM and NB classifier. The highest mean accuracy obtained was 80.12 % and 86.52 % with an ICA feature vector as shown in table 6 using SVM and NB classifier. With our proposed method, the mean accuracy obtained is 91.23 % with 80 genes and 95.42 % with 90 genes for SVM and NB classification, which shows that the FBFE approach with ICA performs better than the other existing methods.

Figure 9-10

Figure 9 and 10 shows the graph of the average error rate of SVM and NB classifier respectively, for the five datasets with different gene selection methods. It is clearly shown in figure that ICA+FBFE with SVM and NB classifier performs better than other gene selection methods because of the reduced error rate, which shows the significance of the proposed method with the other existing methods. It is evident from the graph that when genes are selected, based on FBFE from PCA then the percentage error rate is minimized, which shows that FBFE with PCA performs better than PCA method with SVM and NB classifier.

Figure 11 - 15

For further analysis, AUC (area under the ROC curve) curves obtained on the test set using different numbers of selected features genes (features) with 0.5 threshold value for each datasets are depicted in Figure 11-15. The highest AUC values for each datasets with number of selected genes that gives these highest values are shown in Table 7. From the fig 11-15 we can see that, how the AUC changes with different number of genes. For the Colon data (fig. 11 a-d), the highest value of AUC is 0.91 with 30 genes for SVM classifier and 0.85 with 25 genes for NB classifier. For Acute Leukemia dataset, as the value of selected gene set increases from 30 to 35, AUC also increases from 0.93 to 0.94 for SVM classifier, on the other hand with the same increase in selected gene set for NB classifier, AUC decreases from 0.95 to 0.94. Resultantly it is concluded that 35 genes are best for SVM classifier and 30 are best for NB classifier. For Prostate dataset, highest value of AUC obtained with 50 numbers of selected genes for both the classifiers. For High Grade Glioma data, 25 gene set gives the highest value of AUC because further increase in gene, decreases the value of AUC for SVM classifier and for NB classifier 35 selected genes gives the highest value of AUC. From the figure 15 (a-d) for Lung Cancer data it is clear that with 80 number of selected gene set, highest AUC value is found to be 0.91 for SVM classifier and with 90 selected genes highest AUC value is 0.95 for NB classifier. It is immediately apparent from these results that, with this particular setup, we can find the number of selected genes that gives the best classification accuracy. Table 7

Therefore, with this fuzzy backward feature selection procedure, discarding redundant, noise-corrupted or unimportant features, we can reduce the dimensionality of any type of microarray data to speed up the classification process, increase the accuracy rate of the classification and making the computational expenses affordable. 6. Conclusion

This paper presents a fuzzy backward feature elimination approach in ICA feature vector for SVM and NB classification of microarray data where the methodologies involve dimension reduction of microarray data using ICA, followed by the feature selection using FBFE. The approach was tested by classifying five data sets. ROC shows the best subset of genes, which gives the highest classification accuracy for both the classifier of different datasets using proposed approach. The experimental results show that our combination of gene selection methods of an existing algorithm together with SVM and NB classifier is giving better results as compared to other existing approaches. Our experimental results on five microarray datasets demonstrate the effectiveness of the proposed approach in improving the classification performance of SVM and NB classifier in microarray data analysis. It is observed that the proposed method can obtain better classification accuracy with a smaller number of selected genes than the other existing methods, so our proposed method is effective and efficient for SVM and NB classifier.

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1. Fig. 1. Theoretical framework of ICA algorithms of microarray gene expression data

2. Fig. 2. Maximum margin hyperplanes for SVM divides the plane into two classes

3. Fig. 3. Naïve Bayes Classifier

4. Fig. 4. Number of selected genes V/s Classification accuracy using SVM and NB classifier on colon cancer data, based on proposed method.

5. Fig. 5. Number of selected genes V/s Classification accuracy using SVM and NB classifier on acute leukemia data based on proposed method.

6. Fig. 6. Number of selected genes V/s Classification accuracy using SVM and NB classifier on Prostate tumor data, based on proposed feature method.

7. Fig. 7. Number of selected genes V/s Classification accuracy using SVM and NB classifier on High-grade Glioma data, based on proposed method

8. Fig. 8 Number of selected genes V/s Classification accuracy using SVM and NB classifier on a Lung cancer II data, based on proposed method

9. Fig. 9. Average error rate of SVM classifier for the five datasets with different gene selection method.

10. Fig. 10. Average error rate of NB classifier for the five datasets with different gene selection method.

11. Fig. 11 (a-d). AUC curves on the test set for both the classifiers with different numbers of selected genes using proposed approach for colon cancer data.

12. Fig. 12 (a-d). AUC curves on the test set for both the classifiers with different numbers of selected genes using proposed approach for acute leukemia data.

13. Fig. 13 (a-d). AUC curves on the test set for both the classifiers with different numbers of selected genes using proposed approach for Prostate tumor data.

14. Fig. 14 (a-d). AUC curves on the test set for both the classifiers with different numbers of selected genes using proposed approach for High-grade Glioma data.

15. Fig. 15 (a-d). AUC curves on the test set for both the classifiers with different numbers of selected genes using proposed approach for Lung cancer II data.

Table caption (title)

1. Table 1 Summary of five high dimensional biomedical microarray Datasets (Kent ridge online repository)

2. Table 2 Classification result with Colon cancer data.

3. Table 3 Classification result with Acute leukemia data.

4. Table 4 Classification result with Prostate tumor data.

5. Table 5 Classification result with High-grade Glioma data.

6. Table 6 Classification result with Lung cancer II data.

7. Table 7 Highest AUC values for both the classifiers with best values of selected genes using proposed approach for different datasets.

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Table 1: Summary of five high dimensional biomedical microarray Datasets (Kent ridge online repository)

Data set No. of No. of Class balance +/- No. of Short description

classes features samples

Colon cancer (Alon et al., Data collect from colon cancer patient:

1999) 2 2000 (22\40) 62 tumor biopsies showing tumor negative and normal positive biopsies are from health parts of colons of the same patients.

Acute leukemia (Golub et Data collected from bone marrow

al., 1999) 2 7129 (47\25) 72 samples: distinction is between Acute Myeloid Leukemia(AML) and Acute Lymphoblastic Leukemia(ALL) without previous knowledge of these classes.

Prostate tumor (Dinesh Singh et al., 2002) 2 12600 (50\52) 102 Data from prostate tumor samples where by the non-tumor (normal) prostate sample sand tumor samples (cancer) are identified .

High-grade Glioma (C.L. Data collected from brain tumor

2 12625 (28\22) 50 samples: distinction is between

Nutt at al., 2003) glioblastomas and anaplastic oligodendrogliomas.

Lung cancer II (Gorden at Data collected from tissue samples ;

2 12533 (31\150) 181 classification between Malignant

al., 2002) Pleural Mesothelioma (MPM) and Adenocarcinoma(ADCA)of the lung.

S. No. Classifier Method Mean accuracy Variance

1. SVM 88.19 0.061

2. SVM PCA+SVM 75.15 0.053

3. ICA+SVM 79.19 0.052

4. PCA+FBFE+SVM 83.34 0.032

5. ICA+FBFE+SVM 90.09 0.026

1. PCA+NB 76.58 0.074

2. NB ICA+NB 80.81 0.051

3. PCA+FBFE+NB 82.65 0.032

4. ICA+FBFE+NB 85.46 0.012

S. No. Classifier Method Mean accuracy Variance

1. SVM 92.21 0.071

2. SVM PCA+SVM 76.67 0.054

3. ICA+SVM 88.23 0.039

4. PCA+FBFE+SVM 91.23 0.03

5. ICA+FBFE+SVM 94.20 0.013

1. PCA+NB 68.23 0.053

2. NB ICA+NB 86.21 0.051

3. PCA+FBFE+NB 91.42 0.026

4. ICA+FBFE+NB 95.12 0.023

S. No. Classifier Method Mean accuracy Variance

1. SVM 78.43 0.102

2. SVM PCA+SVM 75.43 0.101

3. ICA+SVM 80.45 0.092

4. PCA+FBFE+SVM 83.23 0.076

5. ICA+FBFE+SVM 88.12 0.043

1. PCA+NB 73.23 0.092

2. NB ICA+NB 79.23 0.083

3. PCA+FBFE+NB 83.22 0.052

4. ICA+FBFE+NB 84.12 0.031

S. No. Classifier Method Mean accuracy Variance

1. SVM 69.23 0.067

2. SVM PCA+SVM 69.72 0.042

3. ICA+SVM 70.21 0.043

4. PCA+FBFE+SVM 73.32 0.047

5. ICA+FBFE+SVM 79.21 0.041

1. PCA+NB 69.78 0.032

2. NB ICA+NB 70.20 0.041

3. PCA+FBFE+NB 74.32 0.021

4. ICA+FBFE+NB 76.23 0.020

S. No. Classifier Method Mean accuracy Variance

1. SVM 76.21 0.074

2. SVM PCA+SVM 75.23 0.081

3. ICA+SVM 80.12 0.091

4. PCA+FBFE+SVM 85.21 0.062

5. ICA+FBFE+SVM 91.23 0.024

1. PCA+NB 80.54 0.061

2. NB ICA+ NB 86.52 0.082

3. PCA+FBFE+NB 91.32 0.034

4. ICA+FBFE+NB 95.42 0.011

Table 7 Highest AUC values for both the classifiers with best values of selected features using proposed approach for different datasets.

S.No. Datasets SVM classifier NB classifier

Highest area under the ROC curve Best values of selected features Highest area under the ROC curve Best values of selected features

1. Colon cancer 0.9126 30 0.8566 25

2. Acute leukemia 0.9468 35 0.9536 30

3. Prostate tumor 0.8857 50 0.8427 50

4. High-grade Glioma 0.7933 25 0.7644 35

5. Lung cancer II 0.9144 80 0.9588 90