  Clustering task of mixed data is a challenging problem. In a probabilistic
framework, the main difficulty is due to a shortage of conventional
distributions for such data. In this paper, we propose to achieve the mixed
data clustering with a Gaussian copula mixture model, since copulas, and in
particular the Gaussian ones, are powerful tools for easily modelling the
distribution of multivariate variables. Indeed, considering a mixing of
continuous, integer and ordinal variables (thus all having a cumulative
distribution function), this copula mixture model defines intra-component
dependencies similar to a Gaussian mixture, so with classical correlation
meaning. Simultaneously, it preserves standard margins associated to
continuous, integer and ordered features, namely the Gaussian, the Poisson and
the ordered multinomial distributions. As an interesting by-product, the
proposed mixture model generalizes many well-known ones and also provides tools
of visualization based on the parameters. At a practical level, the Bayesian
inference is retained and it is achieved with a Metropolis-within-Gibbs
sampler. Experiments on simulated and real data sets finally illustrate the
expected advantages of the proposed model for mixed data: flexible and
meaningful parametrization combined with visualization features.
