Deterministic annealing approach to fuzzy \(c\)-means clustering based on entropy maximization
type: Item
instance of: scholarly article
title: Deterministic annealing approach to fuzzy \(c\)-means clustering based on entropy maximization
zbMATH Open document ID: 1241.94017
DOI: 10.1155/2011/960635
author: Makoto Yasuda
published in: Advances in Fuzzy Systems
publication date: 2012-03-08T00:00:00Z
review text: Summary: This paper deals with the fuzzy clustering method which combines the deterministic annealing (DA) approach with an entropy, especially the Shannon entropy and the Tsallis entropy. By maximizing the Shannon entropy, the fuzzy entropy, or the Tsallis entropy within the framework of the fuzzy c-means (FCM) method, membership functions similar to the statistical mechanical distribution functions are obtained. We examine characteristics of these entropy-based membership functions from the statistical mechanical point of view. After that, both the Shannon- and Tsallis-entropy-based FCMs are formulated as DA clustering using the very fast annealing (VFA) method as a cooling schedule. Experimental results indicate that the Tsallis-entropy-based FCM is stable with very fast deterministic annealing and suitable for this annealing process.
Mathematics Subject Classification ID: 94A17
Mathematics Subject Classification ID: 62H30
Mathematics Subject Classification ID: 94D05
zbMATH DE Number: 6013310
zbMATH Keywords: fuzzy clustering
zbMATH Keywords: deterministic annealing
zbMATH Keywords: Shannon entropy
zbMATH Keywords: fuzzy entropy
zbMATH Keywords: Tsallis entropy
zbMATH Keywords: fuzzy \(c\)-means
zbMATH Keywords: entropy-based membership functions
Wikidata QID: Q58655038
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/960635
OpenAlex ID: W2022884387
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description: scientific article; zbMATH DE number 6013310