Multi-view Subspace Clustering with Joint Tensor Representation and Indicator Matrix Learning

Multi-view subspace clustering (MVSC), as an extension of single-view subspace clustering, can exploit more information and has achieved excellent performance. In particular, the MVSC methods with sparse and low-rank basing have become a research priority as they can improve the clustering effect in an effective way. However, the following problems still exist: 1) focusing only on the connections between two views, ignoring the relationship of higher-order views; 2) performing representation matrix learning and indicator matrix learning separately, unable to get the clustering result in one step and obtain the global optimal solution. To tackle these issues, a novel sparsity and low-rank based MVSC algorithm is designed. It jointly conducts tensor representation learning and indicator matrix learning. More specifically, the Tensor Nuclear Norm (TNN) is utilized to exploit the relationships among higher-order views; besides, by incorporating the subsequent spectral clustering, the indicator matrix learning is conducted during the optimization framework. An iterative algorithm, the alternating direction method of multipliers (ADMM) is derived for the solving of the proposed algorithm. Experiments over five baseline datasets prove the competitiveness and excellence of the presented method with comparisons to other eight state-of-the-art algorithms.