Paper:

# Characteristics of Rough Set *C*-Means Clustering

## Seiki Ubukata, Keisuke Umado, Akira Notsu, and Katsuhiro Honda

Osaka Prefecture University

1-1 Gakuen-cho, Nakaku, Sakai, Osaka 599-8531, Japan

*C*-means, rough set theory, rough

*C*-means, rough set

*C*-means

Hard *C*-means (HCM), which is one of the most popular clustering techniques, has been extended by using soft computing approaches such as fuzzy theory and rough set theory. Fuzzy *C*-means (FCM) and rough *C*-means (RCM) are respectively fuzzy and rough set extensions of HCM. RCM can detect the positive and the possible regions of clusters by using the lower and the upper areas which are respectively analogous to the lower and the upper approximations in rough set theory. RCM-type methods have the problem that the original definitions of the lower and the upper approximations are not actually used. In this paper, rough set *C*-means (RSCM), which is an extension of HCM based on the original rough set definition, is proposed as a rough set-based counterpart of RCM. Specifically, RSCM is proposed as a clustering model on an approximation space considering a space granulated by a binary relation and uses the lower and the upper approximations of temporal clusters. For this study, we investigated the characteristics of the proposed RSCM through basic considerations, visual demonstrations, and comparative experiments. We observed the geometric characteristics of the examined methods by using visualizations and numerical experiments conducted for the problem of classifying patients as having benign or malignant disease based on a medical dataset. We compared the classification performance by viewing the trade-off between the classification accuracy in the positive region and the fraction of objects classified as being in the positive region.

*C*-Means Clustering,”

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.22, No.4, pp. 551-564, 2018.

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