Maximum Entropy Gibbs Density Modeling for Pattern Classification
Recent studies have shown that the Gibbs density function is a good model for visual patterns and that its parameters can be learned from pattern category training data by a gradient algorithm optimizing a constrained entropy criterion. These studies represented each pattern category by a single den...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2012-12-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/14/12/2478 |
| _version_ | 1811306944595492864 |
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| author | Neila Mezghani Amar Mitiche Mohamed Cheriet |
| author_facet | Neila Mezghani Amar Mitiche Mohamed Cheriet |
| author_sort | Neila Mezghani |
| collection | DOAJ |
| description | Recent studies have shown that the Gibbs density function is a good model for visual patterns and that its parameters can be learned from pattern category training data by a gradient algorithm optimizing a constrained entropy criterion. These studies represented each pattern category by a single density. However, the patterns in a category can be so complex as to require a representation spread over several densities to more accurately account for the shape of their distribution in the feature space. The purpose of the present study is to investigate a representation of visual pattern category by several Gibbs densities using a Kohonen neural structure. In this Gibbs density based Kohonen network, which we call a Gibbsian Kohonen network, each node stores the parameters of a Gibbs density. Collectively, these Gibbs densities represent the pattern category. The parameters are learned by a gradient update rule so that the corresponding Gibbs densities maximize entropy subject to reproducing observed feature statistics of the training patterns. We verified the validity of the method and the efficiency of the ensuing Gibbs density pattern representation on a handwritten character recognition application. |
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| format | Article |
| id | doaj.art-c1e21213ddcf42f0ba623f3db538e71e |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-13T08:54:45Z |
| publishDate | 2012-12-01 |
| publisher | MDPI AG |
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| series | Entropy |
| spelling | doaj.art-c1e21213ddcf42f0ba623f3db538e71e2022-12-22T02:53:21ZengMDPI AGEntropy1099-43002012-12-0114122478249110.3390/e14122478Maximum Entropy Gibbs Density Modeling for Pattern ClassificationNeila MezghaniAmar MiticheMohamed CherietRecent studies have shown that the Gibbs density function is a good model for visual patterns and that its parameters can be learned from pattern category training data by a gradient algorithm optimizing a constrained entropy criterion. These studies represented each pattern category by a single density. However, the patterns in a category can be so complex as to require a representation spread over several densities to more accurately account for the shape of their distribution in the feature space. The purpose of the present study is to investigate a representation of visual pattern category by several Gibbs densities using a Kohonen neural structure. In this Gibbs density based Kohonen network, which we call a Gibbsian Kohonen network, each node stores the parameters of a Gibbs density. Collectively, these Gibbs densities represent the pattern category. The parameters are learned by a gradient update rule so that the corresponding Gibbs densities maximize entropy subject to reproducing observed feature statistics of the training patterns. We verified the validity of the method and the efficiency of the ensuing Gibbs density pattern representation on a handwritten character recognition application.http://www.mdpi.com/1099-4300/14/12/2478maximum entropyKohonen neural networkGibbs densityparameter estimationpattern classificationhandwritten characters |
| spellingShingle | Neila Mezghani Amar Mitiche Mohamed Cheriet Maximum Entropy Gibbs Density Modeling for Pattern Classification Entropy maximum entropy Kohonen neural network Gibbs density parameter estimation pattern classification handwritten characters |
| title | Maximum Entropy Gibbs Density Modeling for Pattern Classification |
| title_full | Maximum Entropy Gibbs Density Modeling for Pattern Classification |
| title_fullStr | Maximum Entropy Gibbs Density Modeling for Pattern Classification |
| title_full_unstemmed | Maximum Entropy Gibbs Density Modeling for Pattern Classification |
| title_short | Maximum Entropy Gibbs Density Modeling for Pattern Classification |
| title_sort | maximum entropy gibbs density modeling for pattern classification |
| topic | maximum entropy Kohonen neural network Gibbs density parameter estimation pattern classification handwritten characters |
| url | http://www.mdpi.com/1099-4300/14/12/2478 |
| work_keys_str_mv | AT neilamezghani maximumentropygibbsdensitymodelingforpatternclassification AT amarmitiche maximumentropygibbsdensitymodelingforpatternclassification AT mohamedcheriet maximumentropygibbsdensitymodelingforpatternclassification |