CHAPTER 11

INTEGRATED DIFFERENTIAL FUZZY CLUSTERING FOR ANALYSIS OF MICROARRAY DATA

INDRAJIT SAHA AND UJJWAL MAULIK

11.1 INTRODUCTION

In recent years, DNA microarrays has been developed as a popular technique for gathering a substantial amount of gene expression data that is necessary to examine complex regulatory behavior of a cell [1]. Microarray gene expression data, consisting of G genes and T time points, is typically organized in a two-dimensional (2D) matrix E = [eij] of size G × T. Each element eij gives the expression level of the it h gene at the jt h time point. Clustering [2–4], an important microarray analysis tool, is used to identify the sets of genes with similar expression profiles. Clustering methods partition the input space into K regions, depending on some similarity–dissimilarity metric, where the value of K may or may not be known a priori. The main objective of any clustering technique is to produce a K × n partition matrix U(X) of the given data set X, consisting of n patterns, . The partition matrix may be represented as and j = 1, 2,…, n, where uk,j is the membership of pattern xj to the kt h cluster.

In 1995, Storn and Price proposed a new floating point encoded evolutionary algorithm for global optimization [5] and named it differential evolution [6,7], ...

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