Kernel two-dimensional ridge regression for subspace clustering. (May 2021)

• Record Type: Journal Article
• Authors: Peng, Chong; Zhang, Qian; Kang, Zhao; Chen, Chenglizhao; Cheng, Qiang
• Is Part Of: Pattern recognition. Volume 113(2021)
• Publication Date: 2021-05
• Subjects: Subspace clustering -- Ridge regression -- 2-dimensional -- Kernel; Pattern perception -- Periodicals; Perception des structures -- Périodiques; Patroonherkenning; 006.4
• DOI: 10.1016/j.patcog.2020.107749
• Languages: English
• ISSNs: 0031-3203

Abstract

Highlights: Unlike existing methods that perform vectorization to 2D data in a pre-processing step, we propose to learn a 2D projection matrix such that the most expressive structural information is retained in the spanned subspaces. The learning of projection and construction of representation are seamlessly integrated, such that these two tasks mutually enhance each other and lead to powerful representation. Kernel method for 2D data is introduced to our model, which explicitly considers nonlinear structures of the data. Efficient optimization algorithm is developed with provable convergence guarantee. The algorithm does not rely on ALM type optimization as existing methods usually do, thus we do not need to introduce additional parameters in ALM framework. Extensive experiments confirm the effectiveness of our method. Abstract: Subspace clustering methods have been extensively studied in recent years. For 2-dimensional (2D) data, existing subspace clustering methods usually convert 2D examples to vectors, which severely damages inherent structural information and relationships of the original data. In this paper, we propose a novel subspace clustering method, named KTRR, for 2D data. The KTRR provides us with a way to learn the most representative 2D features from 2D data in learning data representation. In particular, the KTRR performs 2D feature learning and low-dimensional representation construction simultaneously, which renders the two tasks to mutually enhance each other. 2D kernel is introduced to the KTRR, which renders the KTRR to have enhanced capability of capturing nonlinear relationships from data. An efficient algorithm is developed for its optimization with provable decreasing and convergent property in objective value. Extensive experimental results confirm the effectiveness and efficiency of our method.