Paper:

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

## Tadafumi Kondo and Yuchi Kanzawa

Shibaura Institute of Technology

3-7-5 Toyosu, Koto, Tokyo 135-8548, Japan

*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.

*q*-Divergence,”

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.22, No.4, pp. 524-536, 2018.

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