Finite mixture model of conditional dependencies modes to cluster categorical data.

Matthieu Marbac 1, * Christophe Biernacki 1, 2 Vincent Vandewalle 1
* Auteur correspondant
1 MODAL - MOdel for Data Analysis and Learning
Inria Lille - Nord Europe, LPP - Laboratoire Paul Painlevé - UMR 8524, CERIM - Santé publique : épidémiologie et qualité des soins-EA 2694, Polytech Lille, Université de Lille 1, IUT’A
Abstract : We propose a parsimonious extension of the classical latent class model to cluster categorical data by relaxing the class conditional independence assumption. Under this new mixture model, named Conditional Modes Model, variables are grouped into conditionally independent blocks. The corresponding block distribution is a parsimonious multinomial distribution where the few free parameters correspond to the most likely modality crossings, while the remaining probability mass is uniformly spread over the other modality crossings. Thus, the proposed model allows to bring out the intra-class dependency between variables and to summarize each class by a few characteristic modality crossings. The model selection is performed via a Metropolis-within-Gibbs sampler to overcome the computational intractability of the block structure search. As this approach involves the computation of the integrated complete-data likelihood, we propose a new method (exact for the continuous parameters and approximated for the discrete ones) which avoids the biases of the \textsc{bic} criterion pointed out by our experiments. Finally, the parameters are only estimated for the best model via an \textsc{em} algorithm. The characteristics of the new model are illustrated on simulated data and on two biological data sets. These results strengthen the idea that this simple model allows to reduce biases involved by the conditional independence assumption and gives meaningful parameters. Both applications were performed with the R package \texttt{CoModes}
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Pré-publication, Document de travail
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Contributeur : Matthieu Marbac <>
Soumis le : jeudi 20 février 2014 - 18:05:11
Dernière modification le : mercredi 11 janvier 2017 - 01:06:01
Document(s) archivé(s) le : mardi 20 mai 2014 - 15:51:38


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  • HAL Id : hal-00950112, version 1
  • ARXIV : 1402.5103



Matthieu Marbac, Christophe Biernacki, Vincent Vandewalle. Finite mixture model of conditional dependencies modes to cluster categorical data.. 2014. 〈hal-00950112v1〉



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