Seeking Commonness and Inconsistencies: A Jointly Smoothed Approach to Multi-view Subspace Clustering

Multi-view subspace clustering aims to discover the hidden subspace structures from multiple views for robust clustering, and has been attracting considerable attention in recent years. Despite significant progress, most of the previous multi-view subspace clustering algorithms are still faced with two limitations. First, they usually focus on the consistency (or commonness) of multiple views, yet often lack the ability to capture the cross-view inconsistencies in subspace representations. Second, many of them overlook the local structures of multiple views and cannot jointly leverage multiple local structures to enhance the subspace representation learning. To address these two limitations, in this paper, we propose a jointly smoothed multi-view subspace clustering (JSMC) approach. Specifically, we simultaneously incorporate the cross-view commonness and inconsistencies into the subspace representation learning. The view-consensus grouping effect is presented to jointly exploit the local structures of multiple views to regularize the view-commonness representation, which is further associated with the low-rank constraint via the nuclear norm to strengthen its cluster structure. Thus the cross-view commonness and inconsistencies, the view-consensus grouping effect, and the low-rank representation are seamlessly incorporated into a unified objective function, upon which an alternating optimization algorithm is performed to achieve a robust subspace representation for clustering. Experimental results on a variety of real-world multi-view datasets have confirmed the superiority of the proposed approach.