Robust Least Squares Regression for Subspace Clustering: A Multi-View Clustering Perspective

Abstract

Recently, with the assumption that samples can be reconstructed by themselves, subspace clustering (SC) methods have achieved great success. Generally, SC methods contain some parameters to be tuned, and different affinity matrices can obtain with different parameter values. In this paper, for the first time, we study a method for fusing these different affinity matrices to promote clustering performance and provide the corresponding solution from a multi-view clustering (MVC) perspective. That is, we argue that the different affinity matrices are consistent and complementary, which is similar to the fundamental assumption of MVC methods. Based on this observation, in this paper, we use least squares regression (LSR), which is a typical SC method, as an example since it can be efficiently optimized and has shown good clustering performance and we propose a novel robust least squares regression method from an MVC perspective (RLSR/MVCP). Specifically, we first utilize LSR with different parameter values to obtain different affinity matrices. Then, to fully explore the information contained in these different affinity matrices and to remove noise, we further fuse these affinity matrices into a tensor, which is constrained by the tensor low-rank constraint, i.e., the tensor nuclear norm (TNN). The two steps are combined into a framework that is solved by the augmented Lagrange multiplier (ALM) method. The experimental results on several datasets indicate that RLSR/MVCP has very encouraging clustering performance and is superior to state-of-the-art SC methods.