Reduced-Rank Modeling for High-Dimensional Model-Based Clustering (Journal of Computational Mathematics, 2018)
Model-based clustering is popularly used in statistical literature, which often modelsthe data with a Gaussian mixture model. As a consequence, it requires estimation of alarge amount of parameters, especially when the data dimension is relatively large. In thispaper, reduced-rank model and group-sparsity regularization are proposed to equip withthe model-based clustering, which substantially reduce the number of parameters and thusfacilitate the high-dimensional clustering and variable selection simultaneously. We proposean 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) forsolving 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 isdeveloped for tuning the clustering model. The effectiveness of the proposed method issupported in a variety of simulated and real examples, as well as its asymptotic estimationand selection consistencies.