Fuzzy Clustering Methods for Categorical Multivariate Data Based on q-Divergence

This paper presents two fuzzy clustering algorithms for categorical multivariate data based on q -divergence. First, this study shows that a conventional method for vectorial data can be explained as regularizing another conventional method using q -divergence. Second, based on the known results that Kullback-Leibler (KL)-divergence is generalized into the q -divergence, and two conventional fuzzy clustering methods for categorical multivariate data adopt KL-divergence, two fuzzy clustering algorithms for categorical multivariate data that are based on q -divergence are derived from two optimization problems built by extending the KL-divergence in these conventional methods to the q -divergence. Through numerical experiments using real datasets, the proposed methods outperform the conventional methods in term of clustering accuracy.