Multi-view subspace clustering with Kronecker-basis-representation-based tensor sparsity measure

Multi-view data are popular in many machine learning and computer vision applications. For example, in computer vision fields, one object can be described with images, text or videos. Recently, multi-view subspace clustering approaches, which can make use of the complementary information among different views to improve the performance of clustering, have attracted much attention. In this paper, we propose a novel multi-view subspace clustering method with Kronecker-basis-representation-based tensor sparsity measure (MSC-KBR) to address multi-view subspace clustering problem. In the MSC-KBR model, we first construct a tensor based on the subspace representation matrices of different views, and, then the high-order correlations underlying different views can be explored. We also adopt a novel Kronecker-basis-representation-based tensor sparsity measure (KBR) to the constructed tensor to reduce the redundancy of the learned subspace representations and improve the accuracy of clustering. Different from the traditional unfolding-based tensor norm, KBR can encode both sparsity insights delivered by Tucker and CANDECOMP/PARAFAC decompositions for a general tensor. By using the augmented Lagrangian method, an efficient algorithm is presented to solve the optimization problem of the MSC-KBR model. The experimental results on some datasets show that the proposed MSC-KBR model outperforms many state-of-the-art multi-view clustering approaches.