On Bayesian analysis of a finite generalized Dirichlet mixture via a Metropolis-within-Gibbs sampling

In this paper, we present a fully Bayesian approach for generalized Dirichlet mixtures estimation and selection. The estimation of the parameters is based on the Monte Carlo simulation technique of Gibbs sampling mixed with a Metropolis-Hastings step. Also, we obtain a posterior distribution which i...

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Bibliographic Details
Published in:Pattern analysis and applications : PAA 2009-06, Vol.12 (2), p.151-166
Main Authors: Bouguila, Nizar, Ziou, Djemel, Hammoud, Riad I.
Format: Article
Language:English
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Artificial intelligence
Computer Science
Computer science
control theory
systems
Data processing. List processing. Character string processing
Exact sciences and technology
Learning and adaptive systems
Memory organisation. Data processing
Pattern Recognition
Pattern recognition. Digital image processing. Computational geometry
Software
Theoretical Advances
Theoretical computing
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Summary:In this paper, we present a fully Bayesian approach for generalized Dirichlet mixtures estimation and selection. The estimation of the parameters is based on the Monte Carlo simulation technique of Gibbs sampling mixed with a Metropolis-Hastings step. Also, we obtain a posterior distribution which is conjugate to a generalized Dirichlet likelihood. For the selection of the number of clusters, we used the integrated likelihood. The performance of our Bayesian algorithm is tested and compared with the maximum likelihood approach by the classification of several synthetic and real data sets. The generalized Dirichlet mixture is also applied to the problems of IR eye modeling and introduced as a probabilistic kernel for Support Vector Machines.
ISSN:1433-7541
1433-755X
DOI:10.1007/s10044-008-0111-4