Minimum Spanning Trees for Gene Expression Data Clustering

Abstract

This paper describes a new framework for microarray gene-expression data clustering. The foundation of this framework is a minimum spanning tree (MST) representation of a set of multidimensional gene expression data. 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 multidimensional 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 MSTbased 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 EXCAVATOR. To demonstrate its effectiveness, we have tested it on two data sets, i. e., expression data from yeast Saccharomyces cerevisiae, and Arabidopsis expression data in response to chitin elicitation.