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Entropy and Gravity
Entropy 2012, 14(12), 2478-2491; doi:10.3390/e14122478

Maximum Entropy Gibbs Density Modeling for Pattern Classification

1,* , 2
1 Laboratoire de recherche en imagerie et orthopédie, Centre de recherche du CHUM, École de technologie supérieure, Pavillon J.A. de Sève, 1560, rue Sherbrooke E., Y-1615, Montreal (QC),H2L 4M1, Canada 2 Institut national de la recherche scientifique, INRS-EMT, Place Bonaventure, 800, de La Gauchetière O., Montreal (QC), H5A 1K6, Canada 3 École de technologie supérieure, 1100, Rue Notre-Dame O., Montreal (QC), H3C 1K3, Canada
* Author to whom correspondence should be addressed.
Received: 25 September 2012 / Revised: 19 October 2012 / Accepted: 30 November 2012 / Published: 4 December 2012
(This article belongs to the Special Issue Maximum Entropy Production)
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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.
Keywords: maximum entropy; Kohonen neural network; Gibbs density; parameter estimation; pattern classification; handwritten characters maximum entropy; Kohonen neural network; Gibbs density; parameter estimation; pattern classification; handwritten characters
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Mezghani, N.; Mitiche, A.; Cheriet, M. Maximum Entropy Gibbs Density Modeling for Pattern Classification. Entropy 2012, 14, 2478-2491.

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