l1/2-based penalized clustering with half thresholding algorithm

Clustering is a widely applied method in data analysis. As a novel framework of clustering analysis, penalized clustering bases itself on the sparsity of solution, which contributes to its ability of determining the best number of clusters automatically rather than specified in advance. Moreover, l(1/2) regularization has been recognized extensively in recent studies. Compared with other l(p) (0 < p < 1) regularization, it can always obtain sparser solution. Motivated by these two points, we propose a l(1/2)-basedpenalized clustering model, and further transform it into a more general form by introducing the vector comprising pairwise differences between centroids and an auxiliary transfer matrix composed of identity matrixes and null matrixes. Finally, the transformed model is solved by the efficient half thresholding algorithm, which can not only obtain an exact analytic expression of l(1/2) solutions, but also provide an effective parameter selection strategy. We also prove the convergence of the proposed half thresholding algorithm solving l(1/2)-based penalized clustering model. Lastly but not least importantly, benchmark experiments on both synthesis and real data sets from UCI have been conducted to prove the superiority of the proposed method. (C) 2020 Elsevier B.V. All rights reserved.