Flexible Tensor Learning for Multi-View Clustering With Markov Chain

Multi-view clustering has gained great progress recently, which employs the representations from different views for improving the final performance. In this paper, we focus on the problem of multi-view clustering based on the Markov chain by considering low-rank constraints. Since most existing methods fail to simultaneously characterize the relations among different entries in a tensor from the global perspective and describe local structures of similarity matrices of a tensor, we propose a novel Flexible Tensor Learning for Multi-view Clustering with the Markov chain (FTLMCM) to solve this problem. We also construct transition probability matrices based on the Markov chain to fully utilize the connection between the Markov chain and spectral clustering. Specifically, the low-rank constraints of the tensor, the frontal slices and the lateral slices of the tensor are imposed on the objective function of the proposed method to achieve these goals. Besides, these three constraints can be optimized jointly to achieve mutual refinement. FTLMCM also uses the tensor rotation to better explore the relationships among different views. We formulate FTLMCM as a problem of low-rank tensor recovery and solve it with the augmented Lagrangian multiplier. Experiments on six different benchmark data sets under six metrics demonstrate that the proposed method is able to achieve better clustering performance.