Mixture D-vine model based approach to clustering three-way data

In real life applications data with a complex structure can be often arranged in a three way data structure, these include data coming from longi- tudinal studies of multiple responses, spatiotemporal data or data collecting multivariate repeated measures. A three-way data set is characterized by three modes and namely rows, columns and layers. In these type of data there are two types of dependence: between variable and between temporal (or spatial) dependence. Finite mixtures are often used to perform model based clustering of multivariate datasets, but none of the existing methods are developed to reveal simultaneously these two different type of dependences in three-way data. In order to reveal and fully understand the complex and hidden dependence patterns in a wide class of continuous three-way data structure, we propose a mixture model of multivariate densities having D-vine representations. This model decouples the margins and their dependence structure, making it possible to describe the margins by using different distribution families, including non-Gaussian ones. Again, many possible dependence structures can be studied using different copulas.Parameter estimates from simulated and real datasets finally show the suitability of the proposed procedure.