Anchor Structure Regularization Induced Multi-view Subspace Clustering via Enhanced Tensor Rank Minimization

The tensor-based multi-view subspace clustering algorithms have received widespread attention due to the powerful ability to capture high-order correlation across views. Although such algorithms have achieved remarkable success, they still suffer from three main issues: 1)The extremely high computational complexity makes tensor-based methods difficult to handle large-scale data sets. 2)The subspace-based methods usually ignore the local geometric structure of the original data. 3)The commonly used Tensor Nuclear Norm (TNN) treats different singular values equally and under-penalizes the noise components, resulting in a sub-optimal representation tensor. Being aware of these, we propose Anchor Structure Regularitation Induced Multi-view Subspace Clustering via Enhanced Tensor Rank Minimization (ASR-ETR). Specifically, an anchor-representation tensor is constructed by using the anchor representation strategy rather than the self-representation strategy to reduce the time complexity, and the local geometric structure in the learned anchor-representation tensor is enhanced by adopting the Anchor Structure Regularization (ASR). We further devise an Enhanced Tensor Rank (ETR), which is a tighter surrogate of the tensor rank to effectively capture the multi-view high-order correlation. An efficient iterative optimization algorithm is designed to solve the ASR-ETR, which is time-economical and enjoys favorable convergence. Extensive experimental results on various data sets demonstrate the superiority of the proposed algorithm as compared to state-of-the-art methods.