Novel Mixtures Based on the Dirichlet Distribution: Application to Data and Image Classification

Bouguila, Nizar; Ziou, Djemel; Vaillancourt, Jean

doi:10.1007/3-540-45065-3_15

Cited by 42 publications

(18 citation statements)

References 7 publications

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“…Although model-based classification is usually enjoyed for its multiple advantages, model-based discriminant analysis methods is mostly limited to quantitative data. Some extensions exist to handle categorical data using multinomial (Celeux and Govaert 1991) or Dirichlet (Bouguila et al 2003) distributions for instance. In addition, even in the case of quantitative data, the Gaussian assumption may not be well-suited for the data at hand.…”

Section: Model-based Classificationmentioning

confidence: 99%

Kernel discriminant analysis and clustering with parsimonious Gaussian process models

Bouveyron¹,

Fauvel²,

Girard³

2014

Stat Comput

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International audienceThis work presents a family of parsimonious Gaussian process models which allow to build, from a finite sample, a model-based classifier in an infinite dimensional space. The proposed parsimonious models are obtained by constraining the eigen-decomposition of the Gaussian processes modeling each class. This allows in particular to use non-linear mapping functions which project the observations into infinite dimensional spaces. It is also demonstrated that the building of the classifier can be directly done from the observation space through a kernel function. The proposed classification method is thus able to classify data of various types such as categorical data, functional data or networks. Furthermore, it is possible to classify mixed data by combining different kernels. The methodology is as well extended to the unsupervised classification case. Experimental results on various data sets demonstrate the effectiveness of the proposed method

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Section: Model-based Classificationmentioning

confidence: 99%

Kernel discriminant analysis and clustering with parsimonious Gaussian process models

Bouveyron¹,

Fauvel²,

Girard³

2014

Stat Comput

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“…Indeed, many researchers consider finite Gaussian mixtures for data modeling. The Dirichlet mixture, however, could offer better modeling capabilities as shown in [3][4][5]9,10], where it was used as a parent distribution and not as a prior for different image-processing tasks. In [3,10] finite Dirichlet mixture models were introduced as a flexible approach for data modeling, where a deterministic approach for the estimation of its parameters was proposed.…”

Section: Introductionmentioning

confidence: 98%

Software modules categorization through likelihood and bayesian analysis of finite dirichlet mixtures

Bouguila

Wang

Hamza

2010

Journal of Applied Statistics

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In this paper, we examine deterministic and Bayesian methods for analyzing finite Dirichlet mixtures. The deterministic method is based on the likelihood approach, and the Bayesian approach is implemented using the Gibbs sampler. The selection of the number of clusters for both approaches is based on the Bayesian information criterion, which is equivalent to the minimum description length. Experimental results are presented using simulated data, and a real application for software modules classification is also included.dirichlet distribution, mixture modeling, maximum likelihood, EM, MDL, BIC, Bayesian analysis, Gibbs sampling, Metropolis-Hastings, software modules,

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“…, d − 1 and γ jd = β jd − 1. This distribution is a generalization of the Dirichlet distribution widely studied in [25,26,21]. In [20], the authors developed a hybrid stochastic expectation maximization algorithm (HSEM) to estimate the parameters of the generalized Dirichlet mixture.…”

Section: Introductionmentioning

confidence: 99%

A Bayesian Non-Gaussian Mixture Analysis: Application to Eye Modeling

Bouguila

Ziou

Hammoud

2007

2007 IEEE Conference on Computer Vision and Pattern Recognition

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Many computer vision and pattern recognition problems involve the use of finiteGaussian mixture models. Finite mixture model using generalized Dirichlet distribution has been shown as a robust alternative of normal mixtures. In this paper, we adopt a Bayesian approach for generalized Dirichlet mixture estimation and selection. This approach, offers a solid theoretical framework for combining both the statistical model learning and the knowledge acquisition. The estimation of the parameters is based on the Monte Carlo simulation technique of Gibbs sampling mixed with a Metropolis-Hastings step. For the selection of the number of clusters, we used Bayes factors. We have successfully applied the proposed Bayesian framework to model IR eyes. Experimental results are shown to demonstrate the robustness, efficiency, and accuracy of the algorithm.

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Novel Mixtures Based on the Dirichlet Distribution: Application to Data and Image Classification

Cited by 42 publications

References 7 publications

Kernel discriminant analysis and clustering with parsimonious Gaussian process models

Kernel discriminant analysis and clustering with parsimonious Gaussian process models

Software modules categorization through likelihood and bayesian analysis of finite dirichlet mixtures

A Bayesian Non-Gaussian Mixture Analysis: Application to Eye Modeling

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