Sliced Sparse Gradient Induced Multi-View Subspace Clustering via Tensorial Arctangent Rank Minimization

Multi-view clustering method tries to improve the performance of clustering by using the information existing in different views. The tensorial representation is more suitable to capture the high order correlations across different views while keep local geometrical structure in specific view. In this paper, we propose a sliced sparse gradient induced multi-view subspace clustering method via tensorial arctangent rank minimization, named SSG-TAR method. First, a tensorial arctangent rank (TAR) is defined, which is a tighter surrogate of the tensor rank and more effective to explore the consistency among multiple views. Second, a sliced sparse gradient regularization (SSG) is first proposed to enhance the discrimination between clusters and better capture the complementary information in view-specific feature space. Finally, we unify these two terms together and establish an efficient algorithm to optimize the proposed model. Furthermore, the constructed sequence was proved to converge to the stationary KKT point. We have carried out extensive experiments on ten datasets across different types and sizes to verify the performance of our model. The experimental results show that our method have achieved the state-of-the-art performance.