Two-Way Clustering for Contingency Tables: Maximizing a Dependence Measure

Abstract

We consider the simultaneous clustering of the rows and columns of a contingency table such that the dependence between row clusters and column clusters is maximized in the sense of maximizing a general dependence measure. We use Csiszár's ø-divergence between the given two-way distribution and the independence case with the same margins. This includes the classical $χ$2 measure, Kullback-Leibler's discriminating information, and variation distance. By using the general theory of `convexity-based clustering criteria' (Bock 1992, 2002a, 2002b) we derive a k-means-like clustering algorithm that uses `maximum support-plane partitions' (in terms of likelihood ratio vectors) in the same way as classical SSQ clustering uses `minimum-distance partitions'.