A Maximizing Model of Spherical Bezdek-Type Fuzzy Multi-Medoids Clustering

Abstract

This paper proposes three modifications for the maximizing model of spherical Bezdek-type fuzzy c-means clustering (msbFCM). First, we use multi-medoids instead of centroids (msbFMMdd), which is similar to modifying fuzzy c-means to fuzzy multi-medoids. Second, we kernelize msbFMMdd (K-msbFMMdd). msbFMMdd can only be applied to objects in the first quadrant of the unit hypersphere, whereas its kernelized form can be applied to a wider class of objects. The third modification is a spectral clustering approach to K-msbFMMdd using a certain assumption. This approach improves the local convergence problem in the original algorithm. Numerical examples demonstrate that the proposed methods can produce good results for clusters with nonlinear borders when an adequate parameter value is selected.