On Kernelization for a Maximizing Model of Bezdek-Like Spherical Fuzzy c-Means Clustering

摘要

In this study, we propose three modifications for a maximizing model of spherical Bezdek-type fuzzy c-means clustering (msbFCM). First, we kernel-ize msbFCM (K-msbFCM). The original msbFCM can only be applied to objects on the first quadrant of the unit hypersphere, whereas its kernelized form can be applied to a wider class of objects. The second modification is a spectral clustering approach to K-msbFCM using a certain assumption. This approach solves the local convergence problem in the original algorithm. The third modification is to construct a model providing the exact solution of the spectral clustering approach. Numerical examples demonstrate that the proposed methods can produce good results for clusters with nonlinear borders when an adequate parameter value is selected.