Multi-view clustering aims to take advantage of multiple views information to improve the performance of clustering. Many existing methods compute the affinity matrix by low-rank representation (LRR) and pairwise investigate the relationship between views. However, LRR suffers from the high computational cost in self-representation optimization. Besides, compared with pairwise views, tensor form of all views' representation is more suitable for capturing the high-order correlations among all views. Towards these two issues, in this paper, we propose the unified graph and low-rank tensor learning (UGLTL) for multi-view clustering. Specifically, on the one hand, we learn the view-specific affinity matrix based on projected graph learning. On the other hand, we reorganize the affinity matrices into tensor form and learn its intrinsic tensor based on low-rank tensor approximation. Finally, we unify these two terms together and jointly learn the optimal projection matrices, affinity matrices and intrinsic low-rank tensor. We also propose an efficient algorithm to iteratively optimize the proposed model. To evaluate the performance of the proposed method, we conduct extensive experiments on multiple benchmarks across different scenarios and sizes. Compared with the state-of-the-art approaches, our method achieves much better performance.
Computation of low-rank tensor approximation under existence constraint via a forward-backward algorithm