Cluster Validity Measures for Fuzzy Two-Mode Clustering

Two-mode clustering consists in simultaneously partitioning rows (mode 1, e.g. objects) and columns (mode 2, e.g., variables) of a data matrix. Recently, several soft two-mode clustering techniques have been developed according to the fuzzy approach, but how to determine the optimal numbers of clusters for objects and variables is an open problem not yet investigated. In this paper some new cluster validity measures for fuzzy two-mode clustering are introduced. Such measures, defined in terms of the compactness within each cluster and separation between clusters, can be seen as generalizations of well-known indices widely used in the standard fuzzy clustering framework. The adequacy of these proposals is assessed by means of a simulation study.