Enhanced Multi-View Subspace Clustering via Twist Tensor Nuclear Norm and Constraint Propagation

Abstract

Multi-view subspace clustering (MVSC) can effectively group multi-view data distributed around several low-dimensional subspaces. Although encouraging results, most existing methods suffer from two typical limitations, resulting in clustering performance degradation. They ignore high-order correlations underlying the multi-view data, leading to degeneration of complementary power; in addition, they rely on much prior knowledge (e.g., pairwise constraints) for clustering enhancement. In this paper, a novel algorithm called Enhanced Multi-view Subspace Clustering (EMVSC) is proposed to address both limitations. EMVSC can effectively exploit high-order correlations and optimally use limited prior knowledge for better clustering performance. Specifically, EMVSC imposes twist tensor nuclear norm on multi-view tensor representation constructed by stacking view-specific self-representations; in addition, EMVSC exploits prior knowledge of pairwise constraints from whole dataset by employing constraint propagation, which propagates limited constraint knowledge from constrained samples to unconstrained samples. To efficiently optimize EMVSC, an extended intact augmented Lagrangian method is derived with good convergence. Experimental results on seven standard multi-view databases demonstrate its efficacy.