Revisiting Attack-Caused Structural Distribution Shift in Graph Anomaly Detection

Graph anomaly detection (GAD) under semi-supervised setting poses a significant challenge due to the distinct structural distribution between anomalous and normal nodes. Specifically, anomalous nodes constitute a minority and exhibit high heterophily and low homophily compared to normal nodes, which makes the distribution of neighbors of the two types of nodes close, that is, most of them are composed of normal nodes, which causes the two types of nodes to be difficult to distinguish during the aggregation process. Furthermore, we discover that apart from various time factors and annotation preferences, graph adversarial attacks can lead to and amplify the heterophily difference across training and testing data, which is called structural distribution shift (SDS) in this paper. Current mainstream methods for GAD tend to overlook the SDS problem, resulting in poor generalization performance and limited effectiveness in detecting anomalies. This work solves the problem from a feature view. We observe that the degree of SDS varies between anomalies and normal nodes. Hence to address the issue, the key lies in resisting high heterophily for anomalies meanwhile benefiting the learning of normals from homophily. Since different labels correspond to the difference of critical anomaly features which make great contributions to the GAD, we tease out the anomaly features on which we constrain to mitigate the effect of heterophilous neighbors and make them invariant. However, the prior distribution of anomaly features is dynamic and hard to estimate, we thus devise a prototype vector to infer and update this distribution during training. For normal nodes, we constrain the remaining features to preserve the connectivity of nodes and reinforce the influence of the homophilous neighborhood. We term our proposed framework as G raph D ecomposition N etwork (GDN). To demonstrate the effectiveness of the network, we explain the process of feature decomposition in the spectral domain. Extensive experiments are conducted on four benchmark datasets, including two additional datasets and two used in the preliminary work. To further validate our performance under SDS, we conduct an adversarial attack to incur different heterophily degrees for the training set and the test set. The proposed framework achieves remarkable accuracy and robustness boost in GAD, especially in an SDS environment where anomalies have largely different structural distribution across training and testing environments. Our code is open-sourced in https://github.com/fortunato-all/skl-GDN .