Model-based clustering of Gaussian copulas for mixed data

Matthieu Marbac (1) , Christophe Biernacki (1, 2) , Vincent Vandewalle (1)

1 MODAL - MOdel for Data Analysis and Learning
2 LPP - Laboratoire Paul Painlevé - UMR 8524

A mixture model of Gaussian copulas is presented to cluster mixed data (different kinds of variables simultaneously) where any kinds of variables are allowed if they admit a cumulative distribution function. This approach allows to straightforwardly define simple multivariate intra-class dependency models while preserving any one-dimensional margin distributions of each component of interest for the statistician. Typically in this work, the margin distributions of each component are classical parametric ones in order to facilitate the model interpretation. In addition, the intra-class dependencies are taken into account by the Gaussian copulas which provide one correlation coefficient, having robustness properties, per couple of variables and per class. This model generalizes different existing models defined for homogeneous and mixed variables. The inference is performed via a Metropolis-within-Gibbs sampler in a Bayesian framework. Numerical experiments illustrate the model flexibility even if the data are simulated according to another model. Finally, three applications on real data sets strengthen the idea that the proposed model is of interest, since it reduces the biases of the locally independent model and since it provides a meaningful summary of the data.

Mots clés: Mixture models; Clustering; Gaussian copula; Metropolis-within-Gibbs algorithm; Mixed data; Mixture models.

Domaines: Méthodologie [stat.ME]

Matthieu Marbac, Christophe Biernacki, Vincent Vandewalle. Model-based clustering of Gaussian copulas for mixed data. 2014. ⟨hal-00987760v1⟩