Fuzzifier Selection in Fuzzy C-Means from Cluster Size Distribution Perspective

Zhou, Kaile; Yang, Shanlin

doi:10.15388/Informatica.2019.221

Informatica

Fuzzifier Selection in Fuzzy C-Means from Cluster Size Distribution Perspective

Volume 30, Issue 3 (2019), pp. 613–628

Kaile Zhou Shanlin Yang

https://doi.org/10.15388/Informatica.2019.221

Pub. online: 1 January 2019 Type: Research Article

Open Access

Received
1 August 2018

Accepted
1 March 2019

Published
1 January 2019

Abstract

Fuzzy c-means (FCM) is a well-known and widely applied fuzzy clustering method. Although there have been considerable studies which focused on the selection of better fuzzifier values in FCM, there is still not one widely accepted criterion. Also, in practical applications, the distributions of many data sets are not uniform. Hence, it is necessary to understand the impact of cluster size distribution on the selection of fuzzifier value. In this paper, the coefficient of variation (CV) is used to measure the variation of cluster sizes in a data set, and the difference of coefficient of variation (DCV) is the change of variation in cluster sizes after FCM clustering. Then, considering that the fuzzifier value with which FCM clustering produces minor change in cluster variation is better, a criterion for fuzzifier selection in FCM is presented from cluster size distribution perspective, followed by a fuzzifier selection algorithm called CSD-m (cluster size distribution for fuzzifier selection) algorithm. Also, we developed an indicator called Influence Coefficient of Fuzzifier ($\mathit{ICF}$) to measure the influence of fuzzifier values on FCM clustering results. Finally, experimental results on 8 synthetic data sets and 4 real-world data sets illustrate the effectiveness of the proposed criterion and CSD-m algorithm. The results also demonstrate that the widely used fuzzifier value $m=2$ is not optimal for many data sets with large variation in cluster sizes. Based on the relationship between ${\mathit{CV}_{0}}$ and $\mathit{ICF}$, we further found that there is a linear correlation between the extent of fuzzifier value influence and the original cluster size distributions.

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Biographies

Zhou Kaile

zhoukaile@hfut.edu.cn

K. Zhou received the BS and PhD degrees from the School of Management, Hefei University of Technology, Hefei, China, in 2010 and 2014, respectively. From 2013 to 2014, he was a visiting scholar in the Eller College of Management, The University of Arizona, Tucson, AZ, USA. He is currently an associate professor with the School of Management, Hefei University of Technology. His research interests include clustering algorithm, data analysis, and smart energy management.

Yang Shanlin

yangsl@hfut.edu.cn

S. Yang is currently a distinguished professor with the School of Management, Hefei University of Technology, Hefei, China. He has authored over 300 referred journal papers and over 200 conference papers. His research interests include engineering management, information management, and decision support systems. He is a member of the Chinese Academy of Engineering. He is a fellow of the Asian Pacific Industrial Engineering and Management Society. He is also the vice chairman of the China Branch of the Association of Information Systems.

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Keywords

fuzzy c-means fuzzifier CSD-m algorithm cluster size distribution

Funding

This work is supported by the National Natural Science Foundation of China (Nos. 71822104, 71521001), Anhui Science and Technology Major Project (No. 17030901024), Hong Kong Scholars Program (No. 2017-167), and China Postdoctoral Science Foundation (No. 2017M612072).

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