Sparse model-based clustering of three-way data via lasso-type penalties

TL;DR

This paper introduces a sparse model-based clustering method for three-way data using lasso-type penalties, addressing over-parameterization in matrix Gaussian mixture models and enabling feature selection and cluster-specific structure detection.

Contribution

It proposes a novel sparse clustering approach with tailored penalties for three-way data, improving interpretability and flexibility over existing methods.

Findings

Effective in synthetic data experiments

Successfully applied to crime pattern analysis in US cities

Captures cluster-specific associations and variable importance

Abstract

Mixtures of matrix Gaussian distributions provide a probabilistic framework for clustering continuous matrix-variate data, which are becoming increasingly prevalent in various fields. Despite its widespread adoption and successful application, this approach suffers from over-parameterization issues, making it less suitable even for matrix-variate data of moderate size. To overcome this drawback, 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 degree of sparsity across clusters, allowing to induce parsimony in a flexible manner. Estimation of the model relies on the maximization of a penalized likelihood, with specifically tailored group and graphical lasso penalties. These penalties enable the selection of the most informative features for clustering three-way data where variables are recorded over multiple occasions and allow to capture cluster-specific association structures. The proposed methodology is tested extensively on synthetic data and its validity is demonstrated in application to time-dependent crime patterns in different US cities.