REDUCED-RANK MODELING FOR HIGH-DIMENSIONAL MODEL-BASED CLUSTERING

• 来源期刊: 计算数学（英文版）
• 关键词: Clustering Gaussian mixture model Group Lasso ADMM Reduced-rank model
• 年，卷（期）: 2018,（3）
• 页码范围: 426-440
• 页数: 15页
• 语种: 英文
• DOI: 10.4208/jcm.1708-m2016-0830

摘要

Model-based clustering is popularly used in statistical literature, which often models the data with a Gaussian mixture model. As a consequence, it requires estimation of a large amount of parameters, especially when the data dimension is relatively large. In this paper, reduced-rank model and group-sparsity regularization are proposed to equip with the model-based clustering, which substantially reduce the number of parameters and thus facilitate the high-dimensional clustering and variable selection simultaneously. We propose an EM algorithm for this task, in which the M-step is solved using alternating minimization. One of the alternating steps involves both nonsmooth function and nonconvex constraint, and thus we propose a linearized alternating direction method of multipliers (ADMM) for solving it. This leads to an efficient algorithm whose subproblems are all easy to solve. In addition, a model selection criterion based on the concept of clustering stability is developed for tuning the clustering model. The effectiveness of the proposed method is supported in a variety of simulated and real examples, as well as its asymptotic estimation and selection consistencies.