An optimal hierarchical clustering algorithm for gene expression data

Microarrays are used for measuring expression levels of thousands of genes simultaneously. Clustering algorithms are used on gene expression data to find co-regulated genes. An often used clustering strategy is the Pearson correlation coefficient based hierarchical clustering algorithm presented in [Proc. Nat. Acad. Sci. 95 (25) (1998) 14863-14868], which takes O(N³) time. We note that this run time can be reduced to O(N²) by applying known hierarchical clustering algorithms [Proc. 9th Annual ACM-SIAM Symposium on Discrete Algorithms, 1998, pp. 619-628] to this problem. In this paper, we present an algorithm which runs in O(NlogN) time using a geometrical reduction and show that it is optimal.