Sorted Kernel Matrices as Cluster Validity Indexes.

Two basic issues for data analysis and kernel-machines design are approached in this paper: determining the number of partitions of a clustering task and the parameters of kernels. A distance metric is presented to determine the similarity between kernels and FCM proximity matrices. It is shown that this measure is maximized, as a function of kernel and FCM parameters, when there is coherence with embedded structural information. We show that the alignment function can be maximized according FCM and kernel parameters. The results presented shed some light on the general problem of setting up the number of partitions in a clustering task and in the proper setting of kernel parameters according to structural information. Keywords— Affinity matrix, Clustering, Fuzzy C-Means (FCM), Kernel matrix, Reordering, Sorting.