  In this paper, we address the multi-view subspace clustering problem. Our
method utilizes the circulant algebra for tensor, which is constructed by
stacking the subspace representation matrices of different views and then
rotating, to capture the low rank tensor subspace so that the refinement of the
view-specific subspaces can be achieved, as well as the high order correlations
underlying multi-view data can be explored.} By introducing a recently proposed
tensor factorization, namely tensor-Singular Value Decomposition (t-SVD)
\cite{kilmer13}, we can impose a new type of low-rank tensor constraint on the
rotated tensor to capture the complementary information from multiple views.
Different from traditional unfolding based tensor norm, this low-rank tensor
constraint has optimality properties similar to that of matrix rank derived
from SVD, so the complementary information among views can be explored more
efficiently and thoroughly. The established model, called t-SVD based
Multi-view Subspace Clustering (t-SVD-MSC), falls into the applicable scope of
augmented Lagrangian method, and its minimization problem can be efficiently
solved with theoretical convergence guarantee and relatively low computational
complexity. Extensive experimental testing on eight challenging image dataset
shows that the proposed method has achieved highly competent objective
performance compared to several state-of-the-art multi-view clustering methods.
