Adaptive Topological Graph Learning for Generalized Multi-View Clustering

Graph-based multi-view clustering methods construct affinity graphs to depict the potential cluster structure in given data and further partition them into respective groups without the supervision of labels. However, affinity graphs constructed by most of the existing methods lack the ability to precisely reflect the cluster structure of the original data, and fail to recover similarity information when there are missing instances involved. Additionally, current methods mainly employ pairwise relationships between instances to build the affinity graphs but ignore topological relationships, which causes insufficient use of underlying information and results in inferior results. To overcome these shortcomings, in this paper, we propose a novel graph learning method, which is enabled to solve a more general multi-view clustering (MVC) problem, i.e., MVC with probable missing instances. Specifically, a rank-constraint affinity learning method, which is capable to deal with both fully observed and partially observed data, is put forward to preserve similarity between existing instances and infer the similarity related to the missing instances. Moreover, a topological constraint is introduced on the learned affinity matrix, so that more comprehensive information, rather than limited pairwise relationships only, is embraced in each entry of the affinity matrix. Importantly, this is the first work using topological structure to conduct both complete and incomplete multi-view clustering in one unified learning framework. Extensive experiments under both complete and incomplete situations validate the effectiveness of our proposed method when compared to other state-of-the-art multi-view clustering algorithms. Our code has been released at https://github.com/WenjueHE/ATGL_GMVC.