Vine copula mixture models and clustering for non-Gaussian data

Abstract

The majority of finite mixture models suffer from not allowing asymmetric tail dependencies within components and not capturing non-elliptical clusters in clustering applications. Since vine copulas are very flexible in capturing these dependencies, a novel vine copula mixture model for continuous data is proposed. The model selection and parameter estimation problems are discussed, and further, a new model-based clustering algorithm is formulated. The use of vine copulas in clustering allows for a range of shapes and dependency structures for the clusters. The simulation experiments illustrate a significant gain in clustering accuracy when notably asymmetric tail dependencies or/and non-Gaussian margins within the components exist. The analysis of real data sets accompanies the proposed method. The model-based clustering algorithm with vine copula mixture models outperforms others, especially for the non-Gaussian multivariate data.