A Novel Convex Clustering Method for High-Dimensional Data Using Semiproximal ADMM. (21st September 2020)

• Record Type: Journal Article
• Authors: Chen, Huangyue; Kong, Lingchen; Li, Yan
• Other Names: Smolka Bogdan Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2020(2020)
• Publication Date: 2020-09-21
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2020/9216351
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : Clustering is an important ingredient of unsupervised learning; classical clustering methods include K-means clustering and hierarchical clustering. These methods may suffer from instability because of their tendency prone to sink into the local optimal solutions of the nonconvex optimization model. In this paper, we propose a new convex clustering method for high-dimensional data based on the sparse group lasso penalty, which can simultaneously group observations and eliminate noninformative features. In this method, the number of clusters can be learned from the data instead of being given in advance as a parameter. We theoretically prove that the proposed method has desirable statistical properties, including a finite sample error bound and feature screening consistency. Furthermore, the semiproximal alternating direction method of multipliers is designed to solve the sparse group lasso convex clustering model, and its convergence analysis is established without any conditions. Finally, the effectiveness of the proposed method is thoroughly demonstrated through simulated experiments and real applications.