Latent multi-view self-representations for clustering via the tensor nuclear norm

How to design effective multi-view subspace clustering (MVSC) algorithms has recently become a research hotspot. In this paper, we propose a new MVSC algorithm, termed latent multi-view self-representation for clustering via the tensor nuclear norm (LMVS/TNN), which can seamlessly unify multi-view clustering and dimensionality reduction into a framework. Specifically, for each view data, LMVS/TNN learns the transformed data from the original space, which can maintain the original manifold structure, and each subspace representation matrix from the transformed latent space simultaneously. Furthermore, to use the high-order correlations and complementary information from multi-view data, LMVS/TNN constructs a third-order tensor by taking the representation matrix extracted from the transformed latent space as the frontal slice of the third-order tensor and the tensor is constrained by a new low-rank tensor constraint, i.e., the tensor nuclear norm (TNN). In addition, based on the augmented Lagrangian scheme, we develop an efficient procedure to solve LMVS/TNN. To verify the performance of LMVS/TNN, we conduct experiments on public datasets and find that LMVS/TNN outperforms some representative clustering algorithms.