Due to the emergency of multi-view graph data, considerable attention is focused on the multi-view graph clustering. Although great efforts have been made in developing the multi-view graph clustering methods, most of them implicitly follow the homophily assumption, where the connected nodes with edges tend to be in the same category. As a matter of fact, such an ideal assumption is hard to be satisfied in the real-world graph data, and there are some heterogeneous edges connecting dissimilar nodes in graph. How to well consider the homophily and refine the noisy/heterogeneous edges in multi-view graph clustering still remains an under-explored challenge. Therefore, in this paper, we propose a Homophily-enhanced Adaptive Graph Refinement for Multi-view Graph Clustering (HomoMGC) method, where an adaptive graph refinement strategy is seamlessly designed. Specifically, a feature-oriented graph is constructed based on the shared feature, and an integrated graph is computed by averagely fusing all the input adjacent graphs. Then, the feature-oriented graph and integrated graph are stacked into a graph tensor with a low-rank tensor constraint, where a refined affinity probability matrix can be adaptively recovered from the integrated graph by considering multiple graph information as well as the semantics features. Extensive experiments on several benchmark datasets demonstrate the superiority of HomoMGC compared with the state-of-the-art graph clustering methods. For the code reproducibility, the source code of HomoMGC is public available at https://github.com/ManshengChen/Code-for-HomoMGc-master.

Although previous graph-based multi-view clustering (MVC) algorithms have gained significant progress, most of them are still faced with three limitations. First, they often suffer from high computational complexity, which restricts their applications in large-scale scenarios. Second, they usually perform graph learning either at the single-view level or at the view-consensus level, but often neglect the possibility of the joint learning of single-view and consensus graphs. Third, many of them rely on the k -means for discretization of the spectral embeddings, which lack the ability to directly learn the graph with discrete cluster structure. In light of this, this article presents an efficient MVC approach via u nified and d iscrete b ipartite g raph l earning (UDBGL). Specifically, the anchor-based subspace learning is incorporated to learn the view-specific bipartite graphs from multiple views, upon which the bipartite graph fusion is leveraged to learn a view-consensus bipartite graph with adaptive weight learning. Furthermore, the Laplacian rank constraint is imposed to ensure that the fused bipartite graph has discrete cluster structures (with a specific number of connected components). By simultaneously formulating the view-specific bipartite graph learning, the view-consensus bipartite graph learning, and the discrete cluster structure learning into a unified objective function, an efficient minimization algorithm is then designed to tackle this optimization problem and directly achieve a discrete clustering solution without requiring additional partitioning, which notably has linear time complexity in data size. Experiments on a variety of multi-view datasets demonstrate the robustness and efficiency of our UDBGL approach. The code is available at https://github.com/huangdonghere/UDBGL.