Model-based clustering of functional data via mixtures of t distributions

Abstract

We propose a procedure, called T-funHDDC, for clustering multivariate functional data with outliers which extends the functional high dimensional data clustering (funHDDC) method (Schmutz et al. in Comput Stat 35:1101–1131, 2020) by considering a mixture of multivariate t distributions. We define a family of latent mixture models following the approach used for the parsimonious models considered in funHDDC and also constraining or not the degrees of freedom of the multivariate t distributions to be equal across the mixture components. The parameters of these models are estimated using an expectation maximization algorithm. In addition to proposing the T-funHDDC method, we add a family of parsimonious models to C-funHDDC, which is an alternative method for clustering multivariate functional data with outliers based on a mixture of contaminated normal distributions (Amovin-Assagba et al. in Comput Stat Data Anal 174:107496, 2022). We compare T-funHDDC, C-funHDDC, and other existing methods on simulated functional data with outliers and for real-world data. T-funHDDC outperforms funHDDC when applied to functional data with outliers, and its good performance makes it an alternative to C-funHDDC. We also apply the T-funHDDC method to the analysis of traffic flow in Edmonton, Canada.