Statistical Mechanical Analysis of Fuzzy Clustering Based on Fuzzy Entropy

Makoto YASUDA  Takeshi FURUHASHI  Shigeru OKUMA  

Publication
IEICE TRANSACTIONS on Information and Systems   Vol.E90-D   No.6   pp.883-888
Publication Date: 2007/06/01
Online ISSN: 1745-1361
DOI: 10.1093/ietisy/e90-d.6.883
Print ISSN: 0916-8532
Type of Manuscript: PAPER
Category: Computation and Computational Models
Keyword: 
deterministic annealing,  fuzzy entropy,  fuzzy clustering,  fuzzy c-means,  Fermi-Dirac statistics,  

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Summary: 
This paper deals with statistical mechanical characteristics of fuzzy clustering regularized with fuzzy entropy. We obtain the Fermi-Dirac distribution function as a membership function by regularizing the fuzzy c-means with fuzzy entropy. Then we formulate it as a direct annealing clustering, and examine the meanings of Fermi-Dirac function and fuzzy entropy from a statistical mechanical point of view, and show that this fuzzy clustering method is none other than the Fermi-Dirac statistics.