Open-Set Graph Anomaly Detection via Normal Structure Regularisation

This paper considers an under-explored Graph Anomaly Detection (GAD) task, namely open-set GAD, which aims to detect anomalous nodes using a small number of labelled training normal and anomaly nodes (known as seen anomalies) that cannot illustrate all possible inference-time abnormalities. The task has attracted growing attention due to the availability of anomaly prior knowledge from the label information that can help to substantially reduce detection errors. However, current methods tend to over-emphasise fitting the seen anomalies, leading to a weak generalisation ability to detect unseen anomalies, i.e., those that are not illustrated by the labelled anomaly nodes. Further, they were introduced to handle Euclidean data, failing to effectively capture important non-Euclidean features for GAD. In this work, we propose a novel open-set GAD approach, namely normal structure regularisation (NSReg), to leverage the rich normal graph structure embedded in the labelled nodes to tackle the aforementioned two issues. In particular, NSReg trains an anomaly-discriminative supervised graph anomaly detector, with a plug-and-play regularisation term to enforce compact, semantically-rich representations of normal nodes. To this end, the regularisation is designed to differentiate various types of normal nodes, including labelled normal nodes that are connected in their local neighbourhood, and those that are not connected. By doing so, it helps incorporate strong normality into the supervised anomaly detector learning, mitigating their overfitting to the seen anomalies. Extensive empirical results on real-world datasets demonstrate the superiority of our proposed NSReg for open-set GAD.