Graph-based multi-view clustering method has attracted considerable attention in multi-media data analyse community due to its good clustering performance and efficiency in characterizing the relationship between data. But the existing graph-based clustering methods still have many shortcomings. Firstly, they have high computational complexity due to the eigenvalue decomposition. Secondly, the complementary information and spatial structure embedded in different views can affect the clustering performance. However, some existing graph-based clustering methods do not consider these two points. In this article, we use the anchor graphs of different views as input, which effectively reduces the computational complexity. And then we explicitly consider the complementary information and spatial structure between anchor graphs of different views by minimizing the tensor Schatten$p$-norm, aiming to achieve a better tensor with low-rank approximation. Finally, we learn the view-consensus anchor graph with connectivity constraints, which can directly indicate clusters by self-weighted strategy. An efficient alternating algorithm is then derived to optimize the proposed multi-view special clustering model. Furthermore, the constructed sequence was proved to converge to the stationary KKT point. Experiments show that our proposed method not only reduces the time cost, but also outperforms the most advanced methods.

Despite the promising preliminary results, tensor-singular value decomposition (t-SVD)-based multiview subspace is incapable of dealing with real problems, such as noise and illumination changes. The major reason is that tensor-nuclear norm minimization (TNNM) used in t-SVD regularizes each singular value equally, which does not make sense in matrix completion and coefficient matrix learning. In this case, the singular values represent different perspectives and should be treated differently. To well exploit the significant difference between singular values, we study the weighted tensor Schatten p -norm based on t-SVD and develop an efficient algorithm to solve the weighted tensor Schatten p -norm minimization (WTSNM) problem. After that, applying WTSNM to learn the coefficient matrix in multiview subspace clustering, we present a novel multiview clustering method by integrating coefficient matrix learning and spectral clustering into a unified framework. The learned coefficient matrix well exploits both the cluster structure and high-order information embedded in multiview views. The extensive experiments indicate the efficiency of our method in six metrics.