Clustering gene expression data using a graph-theoretic approach: an application of minimum spanning trees.

Abstract

Gene expression data clustering provides a powerful tool for studying functional relationships of genes in a biological process. Identifying correlated expression patterns of genes represents the basic challenge in this clustering problem. This paper describes a new framework for representing a set of multi-dimensional gene expression data as a Minimum Spanning Tree (MST), a concept from the graph theory. A key property of this representation is that each cluster of the expression data corresponds to one subtree of the MST, which rigorously converts a multi-dimensional clustering problem to a tree partitioning problem. We have demonstrated that though the inter-data relationship is greatly simplified in the MST representation, no essential information is lost for the purpose of clustering. Two key advantages in representing a set of multi-dimensional data as an MST are: (1) the simple structure of a tree facilitates efficient implementations of rigorous clustering algorithms, which otherwise are highly computationally challenging; and (2) as an MST-based clustering does not depend on detailed geometric shape of a cluster, it can overcome many of the problems faced by classical clustering algorithms. Based on the MST representation, we have developed a number of rigorous and efficient clustering algorithms, including two with guaranteed global optimality. We have implemented these algorithms as a computer software EXpression data Clustering Analysis and VisualizATiOn Resource (EXCAVATOR). To demonstrate its effectiveness, we have tested it on three data sets, i.e. expression data from yeast Saccharomyces cerevisiae, expression data in response of human fibroblasts to serum, and Arabidopsis expression data in response to chitin elicitation. The test results are highly encouraging. EXCAVATOR is available on request from the authors.