Paper:

# Fuzzy Clustering Method for Spherical Data Based on *q*-Divergence

## Masayuki Higashi, Tadafumi Kondo, and Yuchi Kanzawa

Shibaura Institute of Technology

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

This study presents a fuzzy clustering algorithm for classifying spherical data based on *q*-divergence. First, it is shown that a conventional method for vectorial data is equivalent to the regularization of another conventional method using *q*-divergence. Next, based on the knowledge that *q*-divergence is a generalization of Kullback-Leibler (KL)-divergence and that there is a conventional fuzzy clustering method for classifying spherical data based on KL-divergence, a fuzzy clustering algorithm for spherical data is derived based on *q*-divergence. This algorithm uses an optimization problem built by extending KL-divergence in the conventional method to *q*-divergence. Finally, some numerical experiments are conducted to verify the proposed methods.

*q*-Divergence,”

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.23, No.3, pp. 561-570, 2019.

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