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.
引用
收藏
页码：370 / 376
页数：6
相关论文
共 31 条
  • [21] irni fuzzy c-means clustering with entropy regulariation, Proc. of the 4th Asian Fuzzy Systems Symposium, pp. 217-221, (2000)
  • [22] Landau L.D., Li fshitz E.M., Statistical Physics (Pari 2), (1980)
  • [23] Li R.-P., Mukaidono M., Gaussian clustering method based on maximum-fuzzv-cnlrnpy interpretation, Fuzzy Sets and Systems, 102, pp. 253-258, (1999)
  • [24] Yao J., Dash M., Tan S.T., Liu H., Entropy-based Tuzy clustering and fozy modeling, Fuzzy Sets and Systems, 113, pp. 381-388, (2000)
  • [25] Greiner W., Nei se L., St«ckcr H., Thermodynamics and Statistical Mechanics, (1995)
  • [26] A Modern Course in Statistical Physics, (1998)
  • [27] Hofmann T, Buhmann J., An optimization approach to unsuperviscd hierarchical texture segmentation, Proc. of the Int. Conf. Image Processing {ICIP'97), (1997)
  • [28] Simulated Annealing: Theory and Applications, (1987)
  • [29] Stanley H.E., Ininxtuction to Phase Transitions and Critical Phenomena, (1971)
  • [30] Yusudu M., Furuhashi T., Malsuzaki M., Okuma S., Fuzzy clustering using fuzzy entropy and heuristic search (in Japanese), Journal of Japan Society for Fuzzy Theory and Systems, 13, 4, pp. 387-396, (2001)
1234