Fuzzy two-mode clustering: How to determine the optimal number of clusters?

Two-mode clustering consists in simultaneously grouping rows and columns of an observed data matrix. In this context, an open problem is how to determine the optimal numbers of clusters of both partitions. The choice should consider the overall compactness and separation of the two-mode partition. In addition, if the fuzzy approach to clustering is adopted, the two membership degree matrices should assist in this task. For this reason, some cluster validity indices, taking into account the two objectives and the partitions’ fuzziness, are introduced and investigated. In particular, the well-known Partition Coefficient, Partition Entropy, Fuzzy Silhouette and Xie and Beni indices for standard (one-mode) fuzzy clustering and the here-proposed Fuzzy pseudo-F index are generalized to the fuzzy two-mode clustering framework. The adequacy of the proposed indices is checked by means of a simulation study and some applications.