Cluster Validity Measures with Kernels and Direct Optimization Algorithms

Abstract

In this paper cluster validity measures are investigated and compared. The studied measures are the sum of the traces of the fuzzy covariances within clusters, Xie-Beni's index, Davies-Bouldin's index, and Fukuyama-Sugeno's measure. These measures are kernelized and applied to the determination of the number of clusters having nonlinear boundaries generated by kernel-based clustering algorithms. We also propose a clustering algorithm using Fukuyama-Sugeno's measure.