Deterministic Annealing Approach to Fuzzy C-Means Clustering Based on Entropy Maximization
This paper is dealing 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-me...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Advances in Fuzzy Systems |
| Online Access: | http://dx.doi.org/10.1155/2011/960635 |
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| _version_ | 1832562630484557824 |
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| author | Makoto Yasuda |
| author_facet | Makoto Yasuda |
| author_sort | Makoto Yasuda |
| collection | DOAJ |
| description | This paper is dealing 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. |
| format | Article |
| id | doaj-art-aa22eb8e490f4515a7adc10a0fe8114c |
| institution | Kabale University |
| issn | 1687-7101 1687-711X |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Fuzzy Systems |
| spelling | doaj-art-aa22eb8e490f4515a7adc10a0fe8114c2025-02-03T01:22:13ZengWileyAdvances in Fuzzy Systems1687-71011687-711X2011-01-01201110.1155/2011/960635960635Deterministic Annealing Approach to Fuzzy C-Means Clustering Based on Entropy MaximizationMakoto Yasuda0Department of Electrical and Computer Engineering, Gifu National College of Technology, Kamimakuwa 2236-2, Motosu, Gifu 501-0495, JapanThis paper is dealing 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.http://dx.doi.org/10.1155/2011/960635 |
| spellingShingle | Makoto Yasuda Deterministic Annealing Approach to Fuzzy C-Means Clustering Based on Entropy Maximization Advances in Fuzzy Systems |
| title | Deterministic Annealing Approach to Fuzzy C-Means Clustering Based on Entropy Maximization |
| title_full | Deterministic Annealing Approach to Fuzzy C-Means Clustering Based on Entropy Maximization |
| title_fullStr | Deterministic Annealing Approach to Fuzzy C-Means Clustering Based on Entropy Maximization |
| title_full_unstemmed | Deterministic Annealing Approach to Fuzzy C-Means Clustering Based on Entropy Maximization |
| title_short | Deterministic Annealing Approach to Fuzzy C-Means Clustering Based on Entropy Maximization |
| title_sort | deterministic annealing approach to fuzzy c means clustering based on entropy maximization |
| url | http://dx.doi.org/10.1155/2011/960635 |
| work_keys_str_mv | AT makotoyasuda deterministicannealingapproachtofuzzycmeansclusteringbasedonentropymaximization |