Infinite mixtures of multivariate normal-inverse Gaussian distributions for clustering of skewed data

Abstract

Mixtures of multivariate normal inverse Gaussian (MNIG) distributions can be used to cluster data that exhibit features such as skewness and heavy tails. However, for cluster analysis, using a traditional finite mixture model framework, either the number of components needs to be known $a$-$priori$ or needs to be estimated $a$-$posteriori$ using some model selection criterion after deriving results for a range of possible number of components. However, different model selection criteria can sometimes result in different number of components yielding uncertainty. Here, an infinite mixture model framework, also known as Dirichlet process mixture model, is proposed for the mixtures of MNIG distributions. This Dirichlet process mixture model approach allows the number of components to grow or decay freely from 1 to $\infty$ (in practice from 1 to $N$) and the number of components is inferred along with the parameter estimates in a Bayesian framework thus alleviating the need for model selection criteria. We provide real data applications with benchmark datasets as well as a small simulation experiment to compare with other existing models. The proposed method provides competitive clustering results to other clustering approaches for both simulation and real data and parameter recovery are illustrated using simulation studies.