Graph-based anomaly detection is currently an important research topic in the
field of graph neural networks (GNNs). We find that in graph anomaly detection,
the homophily distribution differences between different classes are
significantly greater than those in homophilic and heterophilic graphs. For the
first time, we introduce a new metric called Class Homophily Variance, which
quantitatively describes this phenomenon. To mitigate its impact, we propose a
novel GNN model named Homophily Edge Generation Graph Neural Network (HedGe).
Previous works typically focused on pruning, selecting or connecting on
original relationships, and we refer to these methods as modifications.
Different from these works, our method emphasizes generating new relationships
with low class homophily variance, using the original relationships as an
auxiliary. HedGe samples homophily adjacency matrices from scratch using a
self-attention mechanism, and leverages nodes that are relevant in the feature
space but not directly connected in the original graph. Additionally, we modify
the loss function to punish the generation of unnecessary heterophilic edges by
the model. Extensive comparison experiments demonstrate that HedGe achieved the
best performance across multiple benchmark datasets, including anomaly
detection and edgeless node classification. The proposed model also improves
the robustness under the novel Heterophily Attack with increased class
homophily variance on other graph classification tasks.

基于图的异常检测是图神经网络领域中一个重要的研究主题。本文引入了一个名为 “类同质性方差” 的新度量方法，量化了图异常检测中不同类之间的同质性分布差异。为了减轻其影响，我们提出一种新型图神经网络模型 —— 同质性边生成图神经网络 (HedGe)。HedGe 使用自注意机制从零开始采样同质性邻接矩阵，并利用特征空间中相关但在原始图中未直接连接的节点。此外，我们修改了损失函数，对模型生成不必要的异质性边进行惩罚。广泛的对比实验表明，HedGe 在多个基准数据集上实现了最佳性能，包括异常检测和无边节点分类。该模型还改善了对新型异质性攻击的鲁棒性，该攻击增加了其他图分类任务中的类同质性方差。

生成优于修改：对抗图形异常检测中的高类同质性方差

Generation is better than Modification: Combating High Class Homophily  Variance in Graph Anomaly Detection

Recently Graph Injection Attack (GIA) emerges as a practical attack scenario
on Graph Neural Networks (GNNs), where the adversary can merely inject few
malicious nodes instead of modifying existing nodes or edges, i.e., Graph
Modification Attack (GMA). Although GIA has achieved promising results, little
is known about why it is successful and whether there is any pitfall behind the
success. To understand the power of GIA, we compare it with GMA and find that
GIA can be provably more harmful than GMA due to its relatively high
flexibility. However, the high flexibility will also lead to great damage to
the homophily distribution of the original graph, i.e., similarity among
neighbors. Consequently, the threats of GIA can be easily alleviated or even
prevented by homophily-based defenses designed to recover the original
homophily. To mitigate the issue, we introduce a novel constraint -- homophily
unnoticeability that enforces GIA to preserve the homophily, and propose
Harmonious Adversarial Objective (HAO) to instantiate it. Extensive experiments
verify that GIA with HAO can break homophily-based defenses and outperform
previous GIA attacks by a significant margin. We believe our methods can serve
for a more reliable evaluation of the robustness of GNNs.

该论文研究了图嵌入攻击对图神经网络的影响，提出了基于同质性的防御方法并设计了一种新的目标函数，实现了对同质性嵌入无感知的控制，该方法在提高对抗攻击的鲁棒性方面有着积极的意义。