Vine copula mixture models and clustering for non-Gaussian data
This work provides a method for improved clustering accuracy for researchers and practitioners working with complex, non-Gaussian multivariate data.
This paper proposes a novel vine copula mixture model to address the limitations of existing finite mixture models in handling asymmetric tail dependencies and non-elliptical clusters. The authors develop a new model-based clustering algorithm and demonstrate significant gains in clustering accuracy in simulations, particularly with asymmetric tail dependencies or non-Gaussian margins.
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.