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Recently there is a growing focus on graph data, and multi-view graph clustering has become a popular area of research interest. Most of the existing methods are only applicable to homophilous graphs, yet the extensive real-world graph data can hardly fulfill the homophily assumption, where the connected nodes tend to belong to the same class. Several studies have pointed out that the poor performance on heterophilous graphs is actually due to the fact that conventional graph neural networks (GNNs), which are essentially low-pass filters, discard information other than the low-frequency information on the graph. Nevertheless, on certain graphs, particularly heterophilous ones, neglecting high-frequency information and focusing solely on low-frequency information impedes the learning of node representations. To break this limitation, our motivation is to perform graph filtering that is closely related to the homophily degree of the given graph, with the aim of fully leveraging both low-frequency and high-frequency signals to learn distinguishable node embedding. In this work, we propose Adaptive Hybrid Graph Filter for Multi-View Graph Clustering (AHGFC). Specifically, a graph joint process and graph joint aggregation matrix are first designed by using the intrinsic node features and adjacency relationship, which makes the low and high-frequency signals on the graph more distinguishable. Then we design an adaptive hybrid graph filter that is related to the homophily degree, which learns the node embedding based on the graph joint aggregation matrix. After that, the node embedding of each view is weighted and fused into a consensus embedding for the downstream task. Experimental results show that our proposed model performs well on six datasets containing homophilous and heterophilous graphs. 

With the increase of multi-view graph data, multi-view graph clustering (MVGC) that can discover the hidden clusters without label supervision has attracted growing attention from researchers. Existing MVGC methods are often sensitive to the given graphs, especially influenced by the low quality graphs, i.e., they tend to be limited by the homophily assumption. However, the widespread real-world data hardly satisfy the homophily assumption. This gap limits the performance of existing MVGC methods on low homophilous graphs. To mitigate this limitation, our motivation is to extract high-level view-common information which is used to refine each view's graph, and reduce the influence of non-homophilous edges. To this end, we propose dual label-guided graph refinement for multi-view graph clustering (DuaLGR), to alleviate the vulnerability in facing low homophilous graphs. Specifically, DuaLGR consists of two modules named dual label-guided graph refinement module and graph encoder module. The first module is designed to extract the soft label from node features and graphs, and then learn a refinement matrix. In cooperation with the pseudo label from the second module, these graphs are refined and aggregated adaptively with different orders. Subsequently, a consensus graph can be generated in the guidance of the pseudo label. Finally, the graph encoder module encodes the consensus graph along with node features to produce the high-level pseudo label for iteratively clustering. The experimental results show the superior performance on coping with low homophilous graph data. The source code for DuaLGR is available at https://github.com/YwL-zhufeng/DuaLGR.