Model-based clustering of categorical data by relaxing conditional independence

Matthieu Marbac 1 Christophe Biernacki 2, 3 Vincent Vandewalle 4, 3
3 MODAL - MOdel for Data Analysis and Learning
LPP - Laboratoire Paul Painlevé - UMR 8524, Inria Lille - Nord Europe, CERIM - Santé publique : épidémiologie et qualité des soins-EA 2694, Polytech Lille, Université de Lille 1, IUT’A
Abstract : In model-based clustering, each cluster is modelled by a parametrised probability distribution function (pdf). In the multivariate quantitative data setting many pdf are available (Gaussian, Student, ...) and allow to take into account correlations between variables inside a cluster. In the multivariate qualitative data setting, there is no natural multivariate pdf. Consequently, the variables are usually supposed independent given the cluster, this model is also called latent class model. The latent class model allows to take into account the main data heterogeneity and often produces good partitions in practice. However, it can suffer from severe bias when variables are correlated inside clusters resulting in a bad partition and often to an over-estimation of the number of clusters. In this talk we will present two parsimonious extensions of the latent class model which relax the cluster conditional independence assumption. In these two models, variables are grouped into independent blocks given the cluster, each block following a parsimonious and interpretable distribution. The first model supposes that the block distribution in a cluster is a mixture of two extreme distributions, which are respectively the independence and the maximum dependency. The second model supposes that the block distribution in a cluster 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. On both cases, parameters are estimated by maximum likelihood using the EM algorithm. The difficult issue of block structure search is solved by a specific MCMC algorithm for each model. When the variables are dependent given the class, these models allow to reduce the biases of the latent class model and in particular to select a more accurate number of clusters.
Type de document :
Communication dans un congrès
Classification Society Meeting, Jun 2015, Hamilton, Ontario, Canada. 2015
Liste complète des métadonnées

Littérature citée [1 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-01238334
Contributeur : Vincent Vandewalle <>
Soumis le : mardi 5 janvier 2016 - 10:48:24
Dernière modification le : mercredi 25 avril 2018 - 14:23:16

Annexe

Identifiants

  • HAL Id : hal-01238334, version 1

Collections

Citation

Matthieu Marbac, Christophe Biernacki, Vincent Vandewalle. Model-based clustering of categorical data by relaxing conditional independence. Classification Society Meeting, Jun 2015, Hamilton, Ontario, Canada. 2015. 〈hal-01238334〉

Partager

Métriques

Consultations de la notice

261

Téléchargements de fichiers

56