Multiview Spectral Clustering via Structured Low-Rank Matrix Factorization.

Multiview data clustering attracts more attention than their single-view counterparts due to the fact that leveraging multiple independent and complementary information from multiview feature spaces outperforms the single one. Multiview spectral clustering aims at yielding the data partition agreement over their local manifold structures by seeking eigenvalue-eigenvector decompositions. Among all the methods, low-rank representation (LRR) is effective, by exploring the multiview consensus structures beyond the low rankness to boost the clustering performance. However, as we observed, such classical paradigm still suffers from the following stand-out limitations for multiview spectral clustering of overlooking the flexible local manifold structure, caused by aggressively enforcing the low-rank data correlation agreement among all views, and such a strategy, therefore, cannot achieve the satisfied between-views agreement; worse still, LRR is not intuitively flexible to capture the latent data clustering structures. In this paper, first, we present the structured LRR by factorizing into the latent low-dimensional data-cluster representations, which characterize the data clustering structure for each view. Upon such representation, second, the Laplacian regularizer is imposed to be capable of preserving the flexible local manifold structure for each view. Third, we present an iterative multiview agreement strategy by minimizing the divergence objective among all factorized latent data-cluster representations during each iteration of optimization process, where such latent representation from each view serves to regulate those from other views, and such an intuitive process iteratively coordinates all views to be agreeable. Fourth, we remark that such data-cluster representation can flexibly encode the data clustering structure from any view with an adaptive input cluster number. To this end, finally, a novel nonconvex objective function is proposed via the efficient alternating minimization strategy. The complexity analysis is also presented. The extensive experiments conducted against the real-world multiview data sets demonstrate the superiority over the state of the arts.