A New Membership Scaling Fuzzy C-Means Clustering Algorithm

• Published in: IEEE transactions on fuzzy systems Vol. 29; no. 9; pp. 2810 - 2818
• Main Authors: Zhou, Shuisheng, Li, Dong, Zhang, Zhuan, Ping, Rui
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.09.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Acceleration; Algorithms; Automobile customizing; Clustering; Clustering algorithms; Convergence; Fuzzy c-means (FCM); Fuzzy systems; Indexes; Iterative methods; membership degree; membership scaling (MS); Robustness; Scaling; Trajectory; triangular inequality
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2020.3003441

Fuzzy c-means (FCM) is one of the most frequently used methods for clustering. However, with increasing amount of data, FCM suffers from slow convergence and a large amount of calculation because all samples are involved in updating the solutions per iteration without considering the current clustering results. In this article, a new membership scaling FCM (MSFCM) is proposed, based on the observation that the samples, whose nearest cluster center is <inline-formula><tex-math notation="LaTeX">\mathbf {v}</tex-math></inline-formula>, aid the convergence of <inline-formula><tex-math notation="LaTeX">\mathbf {v}</tex-math></inline-formula>, whereas the remaining samples prevent the convergence of <inline-formula><tex-math notation="LaTeX">\mathbf {v}</tex-math></inline-formula>. In the new algorithm, many samples whose nearest cluster centers do not change in the next iteration are chosen by using the triangle inequality. A new scheme for scaling the membership degrees of the chosen samples is suggested to boost the effect of the in-cluster samples and to weaken the effect of the out-of-cluster samples in the clustering process. The new scheme not only accelerates the convergence of the algorithm but also maintains the high clustering quality. Many experimental results on synthetic and real-world data sets have verified the effectiveness of the proposed algorithm in improving the speed of the convergence of the fuzzy clustering. In particular, compared with FCM, MSFCM saves at least two thirds of the total rounds of iterations without significantly increasing the cost per iteration.