  Most recently, tensor-SVD is implemented on multi-view self-representation
clustering and has achieved the promising results in many real-world
applications such as face clustering, scene clustering and generic object
clustering. However, tensor-SVD based multi-view self-representation clustering
is proposed originally to solve the clustering problem in the multiple linear
subspaces, leading to unsatisfactory results when dealing with the case of
non-linear subspaces. To handle data clustering from the non-linear subspaces,
a kernelization method is designed by mapping the data from the original input
space to a new feature space in which the transformed data can be clustered by
a multiple linear clustering method. In this paper, we make an optimization
model for the kernelized multi-view self-representation clustering problem. We
also develop a new efficient algorithm based on the alternation direction
method and infer a closed-form solution. Since all the subproblems can be
solved exactly, the proposed optimization algorithm is guaranteed to obtain the
optimal solution. In particular, the original tensor-based multi-view
self-representation clustering problem is a special case of our approach and
can be solved by our algorithm. Experimental results on several popular
real-world clustering datasets demonstrate that our approach achieves the
state-of-the-art performance.
