Pair-copula based mixture models and their application in clustering

• A pair-copula based mixture model.
• Separation of margins and dependence structures of a multivariate distribution.
• Design of an EM parameter estimation framework that allows online selection of margins and copulas.
• Application of pair-copula mixture distribution to the problem of model based clustering.

Finite mixtures are often used to perform model based clustering of multivariate data sets. In real life applications, such data may exhibit complex nonlinear form of dependence among the variables. Also, the individual variables (margins) may follow different families of distributions. Most of the existing mixture models are unable to accommodate these two aspects of the data. This paper presents a finite mixture model that involves a pair-copula based construction of a multivariate distribution. Such a model de-couples the margins and the dependence structures. Hence, the margins can be modeled using different families. Again, many possible dependence structures can also be studied using different copulas. The resulting mixture model (called DVMM) is then capable of capturing a broad family of distributions including non-Gaussian models. Here we study DVMM in the context of clustering of multivariate data. We design an expectation maximization procedure for estimating the mixture parameters. We perform extensive experiments on the basis of a number of well-known data sets. A detailed evaluation of the clustering quality obtained by DVMM in comparison to other mixture models is presented. The experimental results show that the performance of DVMM is quite satisfactory.