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Cluster Size-Constrained Fuzzy C-Means with Density Center Searching
International Journal of Fuzzy Logic and Intelligent Systems 2020;20(4):346-357
Published online December 25, 2020
© 2020 Korean Institute of Intelligent Systems.

Jiarui Li1, Yukio Horiguchi2, and Tetsuo Sawaragi1

1Department of Mechanical Engineering and Science, Graduate School of Engineering, Kyoto University, Kyoto, Japan
2Faculty of Informatics, Kansai University, Osaka, Japan
Correspondence to: Jiarui Li (
Received June 18, 2020; Revised December 7, 2020; Accepted December 15, 2020.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Fuzzy C-means (FCM) has a definite limitation when partitioning a dataset into clusters with varying sizes and densities because it ignores the scale difference in different dimensions of input data objects. To alleviate this cluster size insensitivity, we propose a wrapper algorithm for FCM by introducing cluster size as a priori information and limiting the search direction on the basis of density benchmarks (CSCD-FCM). This method is divided into two stages. The first stage adjusts the position of each cluster while maintaining its shape, and the second stage changes the shape of each cluster while maintaining its center. Both steps modify fuzzy partitions generated by FCM-like soft clustering methods by optimizing a “size-constrained” objective function. Numerical and practical experiments with unbalanced cluster size settings demonstrate the effectiveness of this method for extracting actual cluster structures, as well as achieving the desired cluster populations.
Keywords : Fuzzy C-means, Clustering, Cluster size insensitivity