Adaptive Tensor Rank Approximation for Multi-View Subspace Clustering

Multi-view subspace clustering under a tensor framework remains a challenging problem, which can be potentially applied to image classification, impainting, denoising, etc. There are some existing tensor-based multi-view subspace clustering models mainly making use of the consistency in different views through tensor nuclear norm (TNN). The diversity which means the intrinsic difference in individual view is always ignored. In this paper, a new tensorial multi-view subspace clustering model is proposed, which jointly exploits both the consistency and diversity in each view. The view representation is decomposed into view-consistent part (low-rank part) and view-specific part (diverse part). A tensor adaptive log-determinant regularization (TALR) is imposed on the low-rank part to better relax the tensor multi-rank, and a view-specific sparsity regularization is applied on the diverse part to ensure connectedness property. Although the TALR minimization is not convex, it has a closed-form analytical solution and its convergency is validated mathematically. Extensive evaluations on six widely used clustering datasets are executed and our model is demonstrated to have the superior performance.