Nonconvex low-rank and sparse tensor representation for multi-view subspace clustering

Multi-view subspace clustering has attracted significant attention due to the popularity of multi-view datasets. The effectiveness of the existing multi-view clustering methods highly depends on the quality of the affinity matrix. To derive a high quality affinity matrix, tensor optimization has been explored for multi-view subspace clustering. However, only the global low-rank correlation information among views has been explored, and the local geometric structure has been ignored. In addition, for low-rank tensor approximation learning, the commonly used tensor nuclear norm cannot retain the main information of all views. In this paper, we propose a nonconvex low-rank and sparse tensor representation (NLRSTR) method, which retains the similarity information of the view dimension from global and local perspectives. Specifically, the proposed NLRSTR method imposes nonconvex function and sparse constraint on the self-representation tensor to characterize the high relationship among views. Based on the alternating direction method of multipliers, an effective algorithm is proposed to solve our NLRSTR model. The experimental results on eight datasets show the superiority of the proposed NLRSTR method compared with seventeen state-of-the-art methods.