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.

提出了一种自适应混合图滤波方法（AHGFC）用于多视图图聚类，通过设计图联合处理和聚合矩阵，以使图中的低频和高频信号更可区分，进而基于图联合聚合矩阵学习节点嵌入，实验证明该方法在同质和异质图上表现出色。

同质性相关：面向多视角图聚类的自适应混合图滤波器

Homophily-Related: Adaptive Hybrid Graph Filter for Multi-View Graph  Clustering

Graph Neural Networks (GNNs) achieve state-of-the-art performance on
graph-structured data across numerous domains. Their underlying ability to
represent nodes as summaries of their vicinities has proven effective for
homophilous graphs in particular, in which same-type nodes tend to connect. On
heterophilous graphs, in which different-type nodes are likely connected, GNNs
perform less consistently, as neighborhood information might be less
representative or even misleading. On the other hand, GNN performance is not
inferior on all heterophilous graphs, and there is a lack of understanding of
what other graph properties affect GNN performance.
In this work, we highlight the limitations of the widely used homophily ratio
and the recent Cross-Class Neighborhood Similarity (CCNS) metric in estimating
GNN performance. To overcome these limitations, we introduce 2-hop Neighbor
Class Similarity (2NCS), a new quantitative graph structural property that
correlates with GNN performance more strongly and consistently than alternative
metrics. 2NCS considers two-hop neighborhoods as a theoretically derived
consequence of the two-step label propagation process governing GCN's
training-inference process. Experiments on one synthetic and eight real-world
graph datasets confirm consistent improvements over existing metrics in
estimating the accuracy of GCN- and GAT-based architectures on the node
classification task.

通过介绍 2NCS 方法，本文挖掘了同质网络比率和 Cross-Class 邻域相似性 (CCNS) 等指标的局限性，并在一个合成和 8 个真实图数据集上进行实验，结果表明 2NCS 可以更准确和一致地评估基于 GCN 和 GAT 的体系结构在节点分类任务上的准确性。