Paper:

# Multi-*q* Extension of Tsallis Entropy Based Fuzzy *c*-Means Clustering

## Makoto Yasuda and Yasuyuki Orito

Department of Electrical and Computer Engineering, Gifu National College of Technology, 2236-2 Kamimakuwa, Motosu-shi, Gifu 501-0495, Japan

*c*-means clustering, tsallis entropy, entropy maximization (extremization), multi-

*q*extension

Tsallis entropy is a *q*-parameter extension of Shannon entropy. Based on the Tsallis entropy, we have introduced an entropy maximization method to fuzzy *c*-means clustering (FCM), and developed a new clustering algorithm using a single-*q* value. In this article, we propose a multi-*q* extension of the conventional single-*q* method. In this method, the *q*s are assigned individually to each cluster. Each *q* value is determined so that the membership function fits the corresponding cluster distribution. This is done to improve the accuracy of clustering over that of the conventional single-*q* method. Experiments are performed on randomly generated numerical data and Fisher’s iris dataset, and it is confirmed that the proposed method improves the accuracy of clustering and is superior to the conventional single-*q* method. If the parameters introduced in the proposed method can be optimized, it is expected that the clusters in data distributions that are composed of clusters of various sizes can be determined more accurately.

*q*Extension of Tsallis Entropy Based Fuzzy

*c*-Means Clustering,”

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.18, No.3, pp. 289-296, 2014.

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