基于lasso型惩罚的三路数据稀疏模型聚类
Sparse model-based clustering of three-way data via lasso-type penalties
AI总结：
针对矩阵高斯混合模型的过参数化问题，提出带组lasso和图lasso惩罚的三路数据稀疏模型聚类方法，可灵活实现简约性并捕捉簇特异性关联，经合成数据和美国城市时变犯罪模式应用验证有效。
摘要：
矩阵高斯分布混合为连续矩阵变量数据的聚类提供了概率框架，这类数据在各领域中日益普遍。尽管该方法被广泛采用并成功应用，但存在过参数化问题，即便对于中等规模的矩阵变量数据也不太适用。为克服这一缺陷，我们提出了一种面向三路数据的稀疏模型聚类方法。该方法假设矩阵混合参数是稀疏的，且不同簇的稀疏程度不同，从而能灵活地实现简约性。模型的估计依赖于带专门定制的组lasso和图lasso惩罚的惩罚似然最大化。这些惩罚能够为变量在多个场合被记录的三路数据聚类选择最具信息量的特征，并捕捉特定于簇的关联结构。我们在合成数据上对所提方法进行了广泛测试，并将其应用于美国不同城市的时变犯罪模式，验证了方法的有效性。
英文摘要：
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.
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