Rank Consistency Induced Multiview Subspace Clustering via Low-Rank Matrix Factorization.

Multiview subspace clustering has been demonstrated to achieve excellent performance in practice by exploiting multiview complementary information. One of the strategies used in most existing methods is to learn a shared self-expressiveness coefficient matrix for all the view data. Different from such a strategy, this article proposes a rank consistency induced multiview subspace clustering model to pursue a consistent low-rank structure among view-specific self-expressiveness coefficient matrices. To facilitate a practical model, we parameterize the low-rank structure on all self-expressiveness coefficient matrices through the tri-factorization along with orthogonal constraints. This specification ensures that self-expressiveness coefficient matrices of different views have the same rank to effectively promote structural consistency across multiviews. Such a model can learn a consistent subspace structure and fully exploit the complementary information from the view-specific self-expressiveness coefficient matrices, simultaneously. The proposed model is formulated as a nonconvex optimization problem. An efficient optimization algorithm with guaranteed convergence under mild conditions is proposed. Extensive experiments on several benchmark databases demonstrate the advantage of the proposed model over the state-of-the-art multiview clustering approaches.