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

Cristina Anton () and Iain Smith ()
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Cristina Anton: MacEwan University
Iain Smith: MacEwan University

Advances in Data Analysis and Classification, 2024, vol. 18, issue 3, No 3, 563-595

Abstract: 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.

Keywords: Functional data analysis; Model-based clustering; Multivariate t distributions; EM algorithm; Multivariate functional principal components analysis; 62H30; 68T10; 62F35 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11634-023-00542-w

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