Sparse Model-Based Clustering of Three-Way Data via Lasso-Type Penalties
针对三维矩阵数据聚类中模型参数过多的问题，提出一种稀疏模型聚类方法，通过组Lasso和图Lasso惩罚选择重要特征并识别聚类特定的关联结构，在合成数据和美国多城市犯罪时间模式数据上验证了有效性。
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.