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.

翻译：近期，图数据日益受到关注，多视图图聚类已成为一个热门研究领域。现有方法大多仅适用于同质图，然而现实中广泛的图数据难以满足同质性假设（即相连节点倾向于属于同一类别）。多项研究指出，传统图神经网络（GNN）本质上是低通滤波器，会丢弃图中低频信息以外的信号，因此其在异质图上表现不佳。但在某些图（尤其是异质图）上，忽略高频信息而仅关注低频信息会阻碍节点表示的学习。为突破这一局限，我们的动机是执行与给定图同质度紧密相关的图滤波，旨在充分利用低频和高频信号来学习可区分的节点嵌入。本文提出了一种面向多视图图聚类的自适应混合图滤波器（AHGFC）。具体而言，首先利用固有节点特征与邻接关系设计图联合处理与图联合聚合矩阵，使图中低频与高频信号更易区分；随后构建与同质度相关的自适应混合图滤波器，基于图联合聚合矩阵学习节点嵌入；最后对各视图的节点嵌入进行加权融合，得到用于下游任务的共识嵌入。实验结果表明，所提模型在包含同质图与异质图的六个数据集上均表现优异。