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Phase Transitions in Fuzzy Clustering Based on Fuzzy Entropy
Makoto Yasuda*, Takeshi Furuhashi**, and Shigeru Okuma***
*Dept. of Electrical and Computer Engineering, Gifu National College of Technology, Shinsei-cho, Motosu-gun, Gifu 501-0495, Japan
**Dept. of Information Engineering, Mie University, 1515 Kamihama-cho, Tsu 514-8507, Japan
***Dept. of Electrical Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan
Received:June 30, 2003Accepted:August 26, 2003Published:October 20, 2003
Keywords:deterministic annealing, fuzzy entropy, fuzzy clustering, fuzzy c-means, Fermi-Dirac statistics, phase transition
Abstract
We studied the statistical mechanical characteristics of fuzzy clustering regularized with fuzzy entropy. We obtained Fermi-Dirac distribution as a membership function by regularizing the fuzzy c-means with fuzzy entropy. We then formulated it as direct annealing clustering, and determined the meanings of the Fermi-Dirac function and fuzzy entropy from the statistical mechanical point of view, and showed that this fuzzy clustering is a part of Fermi-Dirac statistics. We also derived the critical temperature at which phase transition occurs in this fuzzy clustering. Then, with a combination of cluster divisions by phase transitions and an adequate division termination condition, we derived fuzzy clustering that automatically determined the number of clusters, as verified by numerical experiments.
Cite this article as:M. Yasuda, T. Furuhashi, and S. Okuma, “Phase Transitions in Fuzzy Clustering Based on Fuzzy Entropy,” J. Adv. Comput. Intell. Intell. Inform., Vol.7 No.3, pp. 370-376, 2003.Data files:
