Multi-View Subspace Clustering via Relaxed L1-Norm of Tensor Multi-Rank

In this paper, we address the multi-view subspace clustering problem. Our method utilize the circulant algebra for tensor, which is constructed by stacking the subspace representation matrices of different views and then shifting, to explore the high order correlations underlying multi-view data. By introducing a recently proposed tensor factorization, namely tensor-Singular Value Decomposition (t-SVD) [16], we can impose a new type of low-rank tensor constraint on the shifted tensor to capture the complementary information from multiple views. Different from traditional unfolding based tensor norm, this low-rank tensor constraint has optimality properties similar to that of matrix rank derived from SVD, so that complementary information among views can be explored more efficiently and thoroughly. The established model, called t-SVD based Multi-view Subspace Clustering (t-SVD-MSC), falls into the applicable scope of augmented Lagrangian method, and its minimization problem can be efficiently solved with theoretical convergence guarantee and relatively low computational complexity. Extensive experimental testing on eight challenging image dataset shows that the proposed method has achieved highly competent objective performance compared to several state-of-the-art multi-view clustering methods.