  This paper explores the problem of multi-view spectral clustering (MVSC)
based on tensor low-rank modeling. Unlike the existing methods that all adopt
an off-the-shelf tensor low-rank norm without considering the special
characteristics of the tensor in MVSC, we design a novel structured tensor
low-rank norm tailored to MVSC. Specifically, we explicitly impose a symmetric
low-rank constraint and a structured sparse low-rank constraint on the frontal
and horizontal slices of the tensor to characterize the intra-view and
inter-view relationships, respectively. Moreover, the two constraints could be
jointly optimized to achieve mutual refinement. On the basis of the novel
tensor low-rank norm, we formulate MVSC as a convex low-rank tensor recovery
problem, which is then efficiently solved with an augmented Lagrange multiplier
based method iteratively. Extensive experimental results on five benchmark
datasets show that the proposed method outperforms state-of-the-art methods to
a significant extent. Impressively, our method is able to produce perfect
clustering. In addition, the parameters of our method can be easily tuned, and
the proposed model is robust to different datasets, demonstrating its potential
in practice.
