Cluster validity for kernel fuzzy clustering

This paper presents cluster validity for kernel fuzzy clustering. First, we describe existing cluster validity indices that can be directly applied to partitions obtained by kernel fuzzy clustering algorithms. Second, we show how validity indices that take dissimilarity (or relational) data D as input can be applied to kernel fuzzy clustering. Third, we present four propositions that allow other existing cluster validity indices to be adapted to kernel fuzzy partitions. As an example of how these propositions are used, five well-known indices are formulated.We demonstrate several indices for kernel fuzzy c-means (kFCM) partitions of both synthetic and real data.