Unsupervised Learning of a Finite Mixture Model Based on the Dirichlet Distribution and Its Application

Bouguila, Nizar; Ziou, Djemel; Vaillancourt, Jean

doi:10.1109/tip.2004.834664

Cited by 167 publications

(70 citation statements)

References 31 publications

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“…In particular, model-based clustering using finite mixtures of distributions was discarded because of the low number of observations (42 experts) and the high dimensionality of the JPDs (121 values). We discussed the possible use of finite mixtures of Dirichlet distributions [44] as the most straightforward model for clustering probability distributions. However, the Dirichlet distribution has some constraints, e.g., its covariance matrix is strictly negative so it cannot model positive correlations between variables.…”

Section: Discussionmentioning

confidence: 99%

“…Also, it is able to formally address the problem of model selection (finding an appropriate number of clusters). Since each of our observations is aJPD, the Dirichlet distribution [44] could be a suitable choice of a probability density function for each component. However, the low number of observations (N e = 42) over the number of variables (r = 121) ruled out the use of this approach, because it is difficult to obtain accurate estimators of a finite mixture model with so few data.…”

Section: Clustering Of Joint Probability Distributionsmentioning

confidence: 99%

See 1 more Smart Citation

Bayesian network modeling of the consensus between experts: An application to neuron classification

López-Cruz

Larrañaga

DeFelipe

et al. 2014

International Journal of Approximate Reasoning

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Neuronal morphology is hugely variable across brain regions and species, and their classifi-cation strategies are a matter of intense debate in neuroscience. GABAergic cortical interneu-rons have been a challenge because it is difficult to find a set of morphological properties which clearly define neuronal types. A group of 48 neuroscience experts around the world were asked to classify a set of 320 cortical GABAergic interneurons according to the main fea-tures of their three-dimensional morphological reconstructions. A methodology for building a model which captures the opinions of all the experts was proposed. First, one Bayesian network was learned for each expert, and we proposed an algorithm for clustering Bayesian networks corresponding to experts with similar behaviors. Then, a Bayesian network which represents the opinions of each group of experts was induced. Finally, a consensus Bayesian multinet which models the opinions of the whole group of experts was built. A thorough analysis of the consensus model identified different behaviors between the experts when classifying the interneurons in the experiment. A set of characterizing morphological traits for the neuronal types was defined by performing inference in the Bayesian multinet. These findings were used to validate the model and to gain some insights into neuron morphology.

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Section: Discussionmentioning

confidence: 99%

Section: Clustering Of Joint Probability Distributionsmentioning

confidence: 99%

Bayesian network modeling of the consensus between experts: An application to neuron classification

López-Cruz

Larrañaga

DeFelipe

et al. 2014

International Journal of Approximate Reasoning

View full text Add to dashboard Cite

show abstract

“…The key issue that the mixture models face is the selection of the component density function, which is estimated by the parametric method with a certain parametric model that fits the distribution of the observed objects. Several models have been chosen, including the t-distribution mixture model by Peer and McLachlan [20], the noncentral t-distribution mixture models by Tsung and Jack [21], the hybrid models based on Dirichlet by Bouguila et al [22], and the hybrid models with Gaussian distribution in broad sense by Fan [23]. These models are usually limited in some acquainted distribution for simplifying the problem to be analyzed, resulting in a great difference between basic assumption of the parametric model and real physical model, i.e., model mismatch.…”

Section: Introductionmentioning

confidence: 99%

Color image segmentation using nonparametric mixture models with multivariate orthogonal polynomials

Liu

Song

Chen

et al. 2011

Neural Comput & Applic

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To solve the problem of over-reliance on a priori assumptions of the parametric methods for finite mixture models and the problem that monic Chebyshev orthogonal polynomials can only process the gray images, a segmentation method of mixture models of multivariate Chebyshev orthogonal polynomials for color image was proposed in this paper. First, the multivariate Chebyshev orthogonal polynomials are derived by the Fourier analysis and tensor product theory, and the nonparametric mixture models of multivariate orthogonal polynomials are proposed. And the mean integrated squared error is used to estimate the smoothing parameter for each model. Second, to resolve the problem of the estimation of the number of density mixture components, the stochastic nonparametric expectation maximum algorithm is used to estimate the orthogonal polynomial coefficient and weight of each model. This method does not require any prior assumptions on the models, and it can effectively overcome the problem of model mismatch. Experimental performance on real benchmark images shows that the proposed method performs well in a wide variety of empirical situations.

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“…This distribution is the univariate case of the Dirichlet distribution which has proven to have high flexibility to model data (Bouguila et al 2004). Indeed, the capacity of an univariate distribution to provide an accurate fit to data depends on its shape.…”

Section: Introductionmentioning

confidence: 99%

Practical Bayesian estimation of a finite beta mixture through gibbs sampling and its applications

2006

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This paper deals with a Bayesian analysis of a finite Beta mixture model. We present approximation method to evaluate the posterior distribution and Bayes estimators by Gibbs sampling, relying on the missing data structure of the mixture model. Experimental results concern contextual and non-contextual evaluations. The non-contextual evaluation is based on synthetic histograms, while the contextual one model the class-conditional densities of pattern-recognition data sets. The Beta mixture is also applied to estimate the parameters of SAR images histograms.

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Unsupervised Learning of a Finite Mixture Model Based on the Dirichlet Distribution and Its Application

Cited by 167 publications

References 31 publications

Bayesian network modeling of the consensus between experts: An application to neuron classification

Bayesian network modeling of the consensus between experts: An application to neuron classification

Color image segmentation using nonparametric mixture models with multivariate orthogonal polynomials

Practical Bayesian estimation of a finite beta mixture through gibbs sampling and its applications

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