A cluster validity index for FCM-type co-clustering

Cluster validation is an important issue in FCM-type clustering applications and many validity indices have been proposed for selecting the optimal fuzzy partition. In most of FCM-type cluster validity indices, the number of clusters is evaluated by considering the partition quality and geometrical features. The quality of memberships was evaluated by the degree of overlapping or the boundary uncertainty, while the geometrical quality was measured by cluster compactness or cluster separation. In this paper, a new approach for FCM-type cluster validation in fuzzy co-clustering is proposed. Because fuzzy co-clustering extracts object-item dual clusters without using prototypes, a new concept of cluster separation is constructed without using the distances between cluster prototypes. The applicability of the new validity index is demonstrated in several numerical experiments including a document clustering application.