Graph-regularized least squares regression for multi-view subspace clustering

Many works have proven that the consistency and differences in multi-view subspace clustering make the clustering results better than the single-view clustering. Therefore, this paper studies the multi-view clustering problem, which aims to divide data points into several groups using multiple features. However, existing multi-view clustering methods fail to capturing the grouping effect and local geometrical structure of the multiple features. In order to solve these problems, this paper proposes a novel multi-view subspace clustering model called graph-regularized least squares regression (GLSR), which uses not only the least squares regression instead of the nuclear norm to generate grouping effect, but also the manifold constraint to preserve the local geometrical structure of multiple features. Specifically, the proposed GLSR method adopts the least squares regression to learn the globally consensus information shared by multiple views and the column-sparsity norm to measure the residual information. Under the alternating direction method of multipliers framework, an effective method is developed by iteratively update all variables. Numerical studies on eight real databases demonstrate the effectiveness and superior performance of the proposed GLSR over eleven state-of-the-art methods.