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Open-Set Graph Anomaly Detection via Normal Structure Regularisation
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Proposes NSReg, a plug-and-play normal-structure regularisation term that trains supervised graph anomaly detectors to better generalise from seen to unseen anomalies by predicting normal-node-oriented relations.
Problem
Open-set graph anomaly detection: supervised GAD models trained on a few labelled (seen) anomalies overfit them and miss unseen anomaly classes, labelling them as normal.
Approach
A regulariser that predicts normality of node pairs involving labelled normal nodes (connected normal pairs = 1, unconnected normal pairs = alpha, normal-to-unlabelled pairs = 0) and shares the representation learner with a supervised AD loss, tightening the normal region in embedding space.
Key results
- On all anomalies, NSReg averages 0.849 AUC-ROC on Photo/Computers/CS/Yelp versus 0.774 for the best competing BCE baseline.
- On unseen anomalies, NSReg averages 0.808 AUC-ROC versus 0.709 for BCE, a gain of roughly 14% over the top competitors as claimed.
- Plugging NSR into DevNet raises average unseen-anomaly AUC-ROC by 0.078 and AUC-PR by 0.088 across four datasets.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add NSR regularization to supervised GAD | supervised graph anomaly detection · Average, all anomalies | AUC-ROC: 0.774±0.024 -> 0.849±0.013 | Helped |
| add NSR regularization to supervised GAD | supervised graph anomaly detection · Average, unseen anomalies | AUC-ROC: 0.709±0.017 -> 0.808±0.021 | Helped |
| replace NSR with a one-class hypersphere objective (ablation) | NSReg · Average, unseen anomalies | AUC-PR: 0.425±0.031 -> 0.265±0.044 | Hurt |
| replace NSR with supervised contrastive learning (ablation) | NSReg · Average, unseen anomalies | AUC-PR: 0.425±0.031 -> 0.327±0.011 | Hurt |
| replace NSR with unsupervised contrastive learning (ablation) | NSReg · Average, unseen anomalies | AUC-PR: 0.425±0.031 -> 0.365±0.030 | Hurt |
| add unconnected normal-node pairs to relation prediction (ablation) | NSR (dual) · Average, unseen anomalies | AUC-PR: 0.405±0.037 -> 0.425±0.031 | Helped |
| add NSR to DevNet | DevNet · Average, all anomalies | AUC-ROC: +0.079 | Helped |
| add NSR to DCI | DCI · Average, all anomalies | AUC-ROC: +0.050 | Helped |
| add NSR to BWGNN | BWGNN · Average, all anomalies | AUC-PR: +0.097 | Helped |
Surprising findings
- Plain BCE is a strong baseline that outperforms most specialised GAD and imbalanced-node-classification methods on all-anomaly AUC-ROC.
- Graph augmentation methods (GraphSMOTE, GraphENS) do not improve generalisation to unseen anomalies over BCE.
Limitations
- Models normality only within the immediate neighbourhood of labelled normal nodes.
- Relation sampling beyond immediate neighbours could add computational overhead.
- Anomaly classes are constructed by adapting imbalanced node classification and binary GAD datasets rather than natural human-annotated classes.
Experimental setup
Datasets: Photo Computers CS Yelp ogbn-arxiv ogbn-proteins T-Finance
Benchmarks: Photo Computers CS Yelp ogbn-arxiv ogbn-proteins T-Finance
Metrics: AUC-ROC AUC-PR
Baselines: DOMINANT GGAN OCGNN CoLA CONDA TAM ADA-GAD PReNet DevNet DCI BWGNN AMNet
Builds on: GraphSAGE DevNet PReNet BWGNN Deep SAD
Closest papers by meaning
- ARC: A Generalist Graph Anomaly Detector with In-Context Learning (NeurIPS 2024 · similarity 0.91)
- Generative Semi-supervised Graph Anomaly Detection (NeurIPS 2024 · similarity 0.91)
- UniGAD: Unifying Multi-level Graph Anomaly Detection (NeurIPS 2024 · similarity 0.89)
- DiffGAD: A Diffusion-based Unsupervised Graph Anomaly Detector (ICLR 2025 · similarity 0.89)
- ADA-GAD: Anomaly-Denoised Autoencoders for Graph Anomaly Detection (AAAI 2024 · similarity 0.89)
- Graph Anomaly Detection as Dynamical Transport: Training-Free Scoring via Empirical Bayes (NeurIPS 2026 · similarity 0.89)
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