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

TL;DR

This paper introduces HedGe, a novel GNN model that generates new low-homophily-variance relationships to improve graph anomaly detection, outperforming existing methods and enhancing robustness against heterophily attacks.

Contribution

The paper proposes HedGe, a new GNN approach that generates relationships to address class homophily variance, differing from prior modification-based methods.

Findings

HedGe achieves state-of-the-art results on multiple benchmark datasets.

HedGe improves robustness under heterophily attack scenarios.

The new metric Class Homophily Variance effectively quantifies homophily distribution differences.

Abstract

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.