Symmetric Multi-View Subspace Clustering With Automatic Neighbor Discovery

Multi-view subspace clustering (MVSC) is a popular area of research that concentrates on partitioning data points from multiple views. It has gained wide attention in recent years due to the ability to handle complex data with diverse features across different views. However, the success of MVSC largely relies on the quality of the learned similarity matrix, and existing methods normally adopt the separate two-step procedures of optimization and symmetrization, which could not guarantee symmetry and adaptive locality of the similarity matrix. To alleviate this issue, in this paper, we propose a novel paradigm called Symmetric Multi-view Subspace Clustering with Automatic Neighbor Discovery (SMSC-AND), which aims at formulating the symmetrization and localization of the ideal similarity matrix into one unified framework. In particular, we theoretically and experimentally demonstrate that SMSC-AND can directly receive the refined symmetric similarity matrix without previous post-processing procedures. Additionally, we propose an automatic neighbor discovery strategy that avoids previous rank constraints or fixed neighbor size, thereby eliminating the requirement for additional hyperparameters. Benefiting from the aforementioned merits, we can directly explore the local structure of the consensus similarity matrix of multi-view data without pre-searching hyperparameters. Comprehensive experimental results on various benchmark datasets have demonstrated the superiority of the proposed algorithm when compared with other MVSC competitors.