Multi-View Subspace Clustering based on Tensor Schatten-p Norm

In this paper, we focus on the multi-view clustering problem. A novel multi-view clustering framework, called multi-view subspace clustering based on tensor Schatten-p norm (MVSC-TSP), is proposed for clustering task. In our method, the tensor Schatten-p norm, which is based on tensor singular value decomposition, is utilized to explore the global low-rank structure of multi-view self-representations. Since 0<; p<; 1, using tensor Schatten-p norm to relax the tensor multi-rank is more effective than the commonly used tensor nuclear norm. Furthermore, we present a new generalized tensor soft thresholding algorithm to solve the tensor Schatten-p norm minimization problem. Based on this, the proposed non-convex optimal problem can be efficiently solved by the alternating direction method of multipliers. Experimental results on image clustering demonstrate that the proposed method is superior to the state-of-the-art methods in term of various evaluation metrics.