On Bezdek-type fuzzy clustering for categorical multivariate data

Abstract

In this study, five co-clustering algorithms based on Bezdek-type fuzzification of fuzzy clustering are propsoed for categorical multivariate data. The algorithms are motivated the fact that, there are only two fuzzy co-clustering methods — entropy-regularization and quadratic regularization — whereas there are three fuzzy clustering methods for vectorial data: entropy-regularization, quadratic regularization, and Bezdek-type fuzzification. The first algorithm proposed forms the basis of other two algorithms. By interpreting the first algorithm as a variant of a maximizing model of fuzzy multi-medoids, the second algorithm, a spectral clustering approach is obtained. Further, by slightly revising the objective function of the first algorithm, the third algorithm, another spectral clustering approach, is also obtained. The fourth algorithm is obtained by Bezdek-type fuzzification for row-membership whereas entropy-regularization for column-mebership. The fifth algorithm is a spectral clustering approach to the fourth algorithm. Numerical examples demonstrate that the proposed algorithms can produce satisfactory results when suitable parameter values are selected.