  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 confirm the
superiority of our approach. Code available:
https://github.com/huangdonghere/JSMC.
