@Article{JCM-36-426,
author = {Yang , LeiWang , Junhui and Ma , Shiqian},
title = {Reduced-Rank Modeling for High-Dimensional Model-Based Clustering},
journal = {Journal of Computational Mathematics},
year = {2018},
volume = {36},
number = {3},
pages = {426--440},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1708-m2016-0830},
url = {http://global-sci.org/intro/article_detail/jcm/12269.html}
}