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 commonly used Tensor Nuclear Norm (TNN) treats different singular values equally and under-penalizes the noise components, resulting in a sub-optimal representation tensor. 3) The subspace-based methods usually ignore the local geometric structure of the original data. 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 an Anchor Structure Regularization (ASR) is employed to enhance the local geometric structure in the learned anchor-representation tensor. We further define an Enhanced Tensor Rank (ETR), which is a tighter surrogate of the tensor rank and more effective to drive the noise out. Moreover, an efficient iterative optimization algorithm is designed to solve the ASR-ETR, which enjoys both linear complexity and favorable convergence. Extensive experimental results on various data sets demonstrate the superiority of the proposed algorithm as compared to state-of-the-art methods.