Phase Transitions in Fuzzy Clustering Based on Fuzzy Entropy | Zendy

Makoto Yasuda | Zendy; Takeshi Furuhashi | Zendy; Shigeru Okuma | Zendy

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Phase Transitions in Fuzzy Clustering Based on Fuzzy Entropy

Author(s) -

Makoto Yasuda,

Takeshi Furuhashi,

Shigeru Okuma

Publication year - 2003

Publication title -

journal of advanced computational intelligence and intelligent informatics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.172

H-Index - 20

eISSN - 1343-0130

pISSN - 1883-8014

DOI - 10.20965/jaciii.2003.p0370

Subject(s) - fuzzy clustering , fuzzy number , cluster analysis , fuzzy logic , statistical physics , mathematics , fuzzy classification , membership function , physics , computer science , artificial intelligence , pattern recognition (psychology) , fuzzy set

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.

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