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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
Inria Lille - Nord Europe, LPP - Laboratoire Paul Painlevé - UMR 8524, METRICS - Evaluation des technologies de santé et des pratiques médicales - ULR 2694, Polytech Lille - École polytechnique universitaire de Lille, Université de Lille, Sciences et Technologies
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.
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Matthieu Marbac, Christophe Biernacki, Vincent Vandewalle. Model-based clustering of categorical data by relaxing conditional independence. Classification Society Meeting, Mc Master University, Jun 2015, Hamilton, Ontario, Canada. ⟨hal-01238334⟩

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