Mixtures of matrix Gaussian distributions provide a probabilistic framework for clustering continuous matrix-variate data, which are increasingly common in various fields. Despite their widespread use and successful applications, these models suffer from over-parameterization, making them not suitable for even moderately sized matrix-variate data. To address this issue, we introduce a sparse model-based clustering approach for three-way data. Our approach assumes that the matrix mixture parameters are sparse and have different degrees of sparsity across clusters, enabling the induction of parsimony in a flexible manner. Estimation relies on the maximization of a penalized likelihood, with specifically tailored group and graphical lasso penalties. These penalties facilitate the selection of the most informative features for clustering three-way data where variables are recorded over multiple occasions, as well as allowing the identification of cluster-specific association structures. We conduct extensive testing of the proposed methodology on synthetic data and validate its effectiveness through an application to time-dependent crime patterns across multiple U.S. cities. Supplementary files for this article are available online.
Sparse model-based clustering of three-way data via lasso-type penalties / A. Cappozzo, A. Casa, M. Fop. - In: JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS. - ISSN 1061-8600. - (2024), pp. 1-71. [Epub ahead of print] [10.1080/10618600.2024.2429705]
Sparse model-based clustering of three-way data via lasso-type penalties
A. CappozzoPrimo
;
2024
Abstract
Mixtures of matrix Gaussian distributions provide a probabilistic framework for clustering continuous matrix-variate data, which are increasingly common in various fields. Despite their widespread use and successful applications, these models suffer from over-parameterization, making them not suitable for even moderately sized matrix-variate data. To address this issue, we introduce a sparse model-based clustering approach for three-way data. Our approach assumes that the matrix mixture parameters are sparse and have different degrees of sparsity across clusters, enabling the induction of parsimony in a flexible manner. Estimation relies on the maximization of a penalized likelihood, with specifically tailored group and graphical lasso penalties. These penalties facilitate the selection of the most informative features for clustering three-way data where variables are recorded over multiple occasions, as well as allowing the identification of cluster-specific association structures. We conduct extensive testing of the proposed methodology on synthetic data and validate its effectiveness through an application to time-dependent crime patterns across multiple U.S. cities. Supplementary files for this article are available online.File | Dimensione | Formato | |
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