Phase Transitions in Fuzzy Clustering Based on Fuzzy Entropy

被引：0
作者：
Yasuda, Makoto [1 ]
Furuhashi, Takeshi [2 ]
Okuma, Shigeru [3 ]
机构：
[1] Depl. of Electrical and Computer Engineering, Gifu National College of Technology, Shinsei-cho, Motosu-gun, Gifu
[2] Dept. of Information Engineering, Mie University, 1515 Kumihama-cho., Tsu
[3] Dept. of Electrical Engineering, Nagoya University, Furo-cho. Chikusa-ku., Nagoya
来源：
Journal of Advanced Computational Intelligence and Intelligent Informatics | 2003年 / 7卷 / 03期
关键词：
deterministic annealing; Fermi-Dirac statistics; fuzzy c-means; fuzzy clustering; fuzzy entropy; phase transition;
D O I：
10.20965/jaciii.2003.p0370
中图分类号：
学科分类号：
摘要：
We studied the statistical mechanical characteristics of fuzzy clustering regularized with fuzzy entropy. We obtained Fermi-Dirac distribution as a membership function by regularizing tbe fuzzy c-means with fuzzy entropy. We then formulated it as direct annealing clustering, and determined the meanings of the Fermi-Pi rac 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. © 2003 Fuji Technology Press. All rights reserved.
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页码：370 / 376
页数：6
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