Vine copula mixture models and clustering for non-Gaussian data

TL;DR

This paper introduces a flexible vine copula mixture model for clustering non-Gaussian data, effectively capturing asymmetric tail dependencies and complex cluster shapes, leading to improved accuracy over existing methods.

Contribution

The paper proposes a novel vine copula mixture model and a corresponding clustering algorithm that better captures complex dependencies and non-elliptical clusters in continuous data.

Findings

Significant improvement in clustering accuracy with asymmetric tail dependencies.

Outperforms existing model-based clustering methods on non-Gaussian data.

Effective in real-world data analysis with complex dependency structures.

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 types of dependencies, we propose a novel vine copula mixture model for continuous data. We discuss the model selection and parameter estimation problems and further formulate a new model-based clustering algorithm. The use of vine copulas in clustering allows for a range of shapes and dependency structures for the clusters. Our 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. We show that the model-based clustering algorithm with vine copula mixture models outperforms the other model-based clustering techniques, especially for the non-Gaussian multivariate data.