Year: 2018
Author: Lei Yang, Junhui Wang, Shiqian Ma
Journal of Computational Mathematics, Vol. 36 (2018), Iss. 3 : pp. 426–440
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1708-m2016-0830
Journal of Computational Mathematics, Vol. 36 (2018), Iss. 3 : pp. 426–440
Published online: 2018-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Clustering Gaussian mixture model Group Lasso ADMM Reduced-rank model.