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DNA microarray technology has made it possible to simultaneously monitor the expression levels of thousands of genes during biological processes and across collections of related samples. However, the large number of genes and the complexity of biological networks greatly increase the challenges of comprehending and interpreting the resulting mass of data, which often consists of millions of measurements. A first step toward addressing this challenge is the use of clustering techniques, which is essential in the data mining process to reveal natural structures and identify interesting patterns in the underlying data. Cluster analysis seeks to partition a given data set into groups based on specified features so that the data points within a group are more similar to each other than the points in different groups. Many conventional clustering algorithms have been adapted or directly applied to gene expression data, and also new algorithms have recently been proposed specifically aiming at gene expression data. These clustering algorithms have been proven useful for identifying biologically relevant groups of genes and samples. A large number of clustering approaches have been proposed for the analysis of gene expression data obtained from microarray experiments. However, the results of the application of standard clustering methods to genes are limited. These limited results are imposed by the existence of a number of experimental conditions where the activity of genes is uncorrelated. A similar limitation exists when clustering of conditions is performed. For this reason, a number of algorithms that perform simultaneous clustering on the row and column dimensions of the gene expression matrix have been proposed to date. This simultaneous clustering, usually designated by biclustering, seeks to find submatrices that are subgroups of genes and subgroups of columns, where the genes exhibit highly correlated activities for every condition. This type of algorithms has also been proposed and used in other fields, such as information retrieval and data mining. In this paper, we first briefly introduce the concepts of microarray technology and discuss the basic elements of clustering on gene expression data. Then, we present specific challenges pertinent to each clustering category and introduce several representative approaches.

Graph Theoretic Techniques for Clustering and Biclustering gene expression data.