Title :

Model-based clustering of Gaussian copulas for mixed data

Author(s) :

Marbac, Matthieu [Auteur]
MOdel for Data Analysis and Learning [MODAL]
Biernacki, Christophe [Auteur]
MOdel for Data Analysis and Learning [MODAL]
Vandewalle, Vincent [Auteur]
MOdel for Data Analysis and Learning [MODAL]

Journal title :

Communications in Statistics - Theory and Methods

Pages :

11635-11656

Publisher :

Taylor & Francis

Publication date :

2017

ISSN :

0361-0926

English keyword(s) :

Metropolis-within-Gibbs algorithm
Gaussian copula
Clustering
Mixed data
Mixture models
Visualization

HAL domain(s) :

Statistiques [stat]/Méthodologie [stat.ME]
Mathématiques [math]/Statistiques [math.ST]

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL