Algorithmic Approaches to Clustering Gene Expression Data

Technologies for generating high-density arrays of cDNAs and oligonucleotides are developing rapidly, and changing the landscape of biological and biomedical research. They enable, for the rst time, a global, simultaneous view on the transcription levels of many thousands of genes, when the cell undergoes speci c conditions or processes. For several organisms that had their genomes completely sequenced, the full set of genes can already be monitored this way today. The potential of such technologies is tremendous: The information obtained by monitoring gene expression levels in di erent developmental stages, tissues types, clinical conditions and di erent organisms can help understanding genes function, gene networks, diagnostic of disease conditions and e ects of medical treatments. Undoubtedly, other applications will emerge in coming years. A key step in the analysis of gene expression data is the identi cation of groups of genes that manifest similar expression patterns. This translates to the algorithmic problem of clustering gene expression data. A clustering problem consists of elements and a characteristic vector for each element. A measure of similarity is de ned between pairs of such vectors. (In gene expression, elements are usually genes, the vector of each gene contains its expression levels under each of the monitored conditions, and similarity can be measured, for example, by the correlation coeÆcient between vectors.) The goal is to partition the elements into subsets, which are called clusters, so that two criteria are satis ed: Homogeneity elements in the same cluster are highly similar to each other; and separation elements from di erent clusters have low similarity to each other. Department of Computer Science, Tel-Aviv University, Tel-Aviv, Israel. fshamir,[email protected].