Among various multi-view clustering approaches, tensor-based multi-view subspace clustering methods aim to explore the high-order correlations across varying views and have achieved encouraging effects. Nevertheless, there are still some demerits in them: (1) View-specific information hinders the mining of global consensus. (2) The local structure inside individual view lacks consideration. (3) Clustering results are not utilized to reversely guide the low-rank tensor optimization. In order to tackle these drawbacks, we propose a unified model termed as Low-rank Tensor Approximation with Local Structure for Multi-view Intrinsic Subspace Clustering. Specifically, the proposed model learns multiple intrinsic subspace representations via the rank preserving decomposition, which is to mitigate the impact of view-specific information on enhancing the global consistency. Then, these intrinsic subspace representations are assembled into a 3-order target tensor with tensor nuclear norm constraint. To preserve the consistent locality, we adopt the manifold regularization to constrain each view when mapping into the intrinsic subspace. Furthermore, since the learned label indicator matrix implicitly characterizes the cluster structure, which is used to guide the optimization of the low-rank tensor representation. Finally, abundant experiments on six real-word datasets demonstrate that the proposed method is superior over other state-of-the-art clustering methods.
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