Orthopartitions and soft clustering: Soft mutual information measures for clustering validation

In this work, we introduce the notion of orthopartition as a generalized partition with uncertainty. Several entropy-based measures are then developed to measure this intrinsic uncertainty, which are in turn applied to soft clustering. An application is explored: the use of the new Soft Mutual Information Measures to evaluate the performances of soft clustering algorithms. The new measures and methods are then tested on standard datasets, showing their applicability to rough clustering