TY - JOUR T1 - Reduced-Rank Modeling for High-Dimensional Model-Based Clustering AU - Yang , Lei AU - Wang , Junhui AU - Ma , Shiqian JO - Journal of Computational Mathematics VL - 3 SP - 426 EP - 440 PY - 2018 DA - 2018/06 SN - 36 DO - http://doi.org/10.4208/jcm.1708-m2016-0830 UR - https://global-sci.org/intro/article_detail/jcm/12269.html KW - Clustering, Gaussian mixture model, Group Lasso, ADMM, Reduced-rank model. AB -

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.