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SpaceGNN: Multi-Space Graph Neural Network for Node Anomaly Detection with Extremely Limited Labels
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Proposes SpaceGNN, an ensemble of Euclidean and hyperbolic/spherical GNNs with learnable curvature, distance-aware propagation, and multi-space ensembling for node anomaly detection under extremely limited labels.
Problem
Node anomaly detection on graphs with extremely limited labels; existing NAD methods embed graphs in a single Euclidean space (or a single fixed-curvature non-Euclidean space) and rely on synthetic/pseudo-label data augmentation, which is shown to be ineffective.
Approach
Learn per-layer curvature via a Learnable Space Projection, weight neighbor messages by a distance-aware coefficient (weighted homogeneity), and ensemble Euclidean, hyperbolic, and spherical GNNs instead of using data augmentation.
Key results
- SpaceGNN reports AUC 0.9389 on Weibo and 0.9400 on T-Finance, and F1 0.8541 on Weibo, in the main random-split table.
- Averaged over 9 datasets, SpaceGNN outperforms the best rival by 8.55% in AUC and 4.31% in F1 (vs. CONSISGAD).
- Ablation on 9 datasets shows removing LSP or DAP lowers AUC and F1 consistently, e.g., Tolokers F1 0.6012 full vs. 0.5560 without LSP.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add learnable space projection (LSP) (ablation) | SpaceGNN · 9 real-world NAD datasets | AUC | Helped |
| add learnable space projection (LSP) (ablation) | SpaceGNN · 9 real-world NAD datasets | F1 | Helped |
| add distance-aware propagation (DAP) (ablation) | SpaceGNN · 9 real-world NAD datasets | AUC | Helped |
| add distance-aware propagation (DAP) (ablation) | SpaceGNN · 9 real-world NAD datasets | F1 | Helped |
| replace the best rival with SpaceGNN | NAD models · 9 real-world datasets | AUC: 8.55% | Helped |
| replace the best rival with SpaceGNN | NAD models · 9 real-world datasets | F1: 4.31% | Helped |
Surprising findings
- Synthetic pseudo-label augmentation (CONSISGAD) produced mostly false anomalous labels even with a fully trained model.
- A plain MLP is surprisingly competitive on several datasets, suggesting naive propagation can hurt NAD performance.
Limitations
- Hyperparameters chosen by validation F1 per dataset via grid search, so per-dataset tuning is required.
- Theoretical results rely on Gaussian feature assumptions and small-covariance approximations.
- Some reported baseline numbers differ between the main and appendix tables, raising consistency concerns.
Experimental setup
Datasets: Weibo Reddit Tolokers Amazon T-Finance YelpChi Questions DGraph-Fin T-Social
Benchmarks: Weibo Reddit Tolokers Amazon T-Finance YelpChi Questions DGraph-Fin T-Social
Metrics: AUC F1
Baselines: MLP GCN GraphSAGE GAT GIN HNN HGCN HYLA AMNet BWGNN GDN SparseGAD
Builds on: HGCN HNN kappa-stereographic model GADBench
Closest papers by meaning
- DiffGAD: A Diffusion-based Unsupervised Graph Anomaly Detector (ICLR 2025 · similarity 0.86)
- ARC: A Generalist Graph Anomaly Detector with In-Context Learning (NeurIPS 2024 · similarity 0.86)
- Rayleigh Quotient Graph Neural Networks for Graph-level Anomaly Detection (ICLR 2024 · similarity 0.86)
- UniFORM: Towards Unified Framework for Anomaly Detection on Graphs (AAAI 2025 · similarity 0.85)
- Self-Discriminative Modeling for Anomalous Graph Detection (ICML 2025 · similarity 0.85)
- Rethinking Reconstruction-based Graph-Level Anomaly Detection: Limitations and a Simple Remedy (NeurIPS 2024 · similarity 0.84)
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