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Rayleigh Quotient Graph Neural Networks for Graph-level Anomaly Detection
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Proposes RQGNN, a spectral GNN for graph-level anomaly detection that explicitly learns the Rayleigh Quotient of graphs and implicitly learns spectral features via Chebyshev wavelet GNN with a Rayleigh-Quotient-weighted pooling and class-balanced focal loss.
Problem
Graph-level anomaly detection on molecular graphs lacks spectral analysis of anomalous graphs; existing spatial GNNs and graph classification models underperform because they do not capture the spectral energy differences between anomalous and normal graphs.
Approach
Shows that accumulated high-frequency spectral energy equals the graph Rayleigh Quotient, then combines an explicit RQ learning branch with a Chebyshev wavelet GNN whose attention pooling weights nodes by the Rayleigh Quotient, trained with a class-balanced focal loss.
Key results
- RQGNN outperforms the best rival iGAD by 1.44% in AUC and 6.74% in Macro-F1 on average across 10 datasets.
- On MCF-7 RQGNN reaches AUC 0.8354 and Macro-F1 0.7394, versus iGAD's 0.8146 and 0.6468.
- RQGNN-1 (average pooling instead of RQ-pooling) and RQGNN-2 (no RQL) remain competitive, and RQGNN improves over RQGNN-1 by 1.76% AUC and 3.92% Macro-F1 on average.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use RQGNN instead of iGAD | Graph-level anomaly detection · 10 real-world datasets | AUC and Macro-F1: +1.44% AUC; +6.74% Macro-F1 | Helped |
| Replace RQ-pooling with average pooling (ablation) | RQGNN · 10 real-world datasets | AUC and Macro-F1: 1.76% AUC; 3.92% Macro-F1 | Hurt |
| Remove the RQL component (ablation) | RQGNN · 10 real-world datasets | AUC and Macro-F1: 0.09% AUC; 1.08% Macro-F1 | Hurt |
| Replace class-balanced focal loss with cross-entropy loss (ablation) | RQGNN · 10 real-world datasets | AUC and Macro-F1 | Hurt |
| Use class-balanced focal loss instead of cross-entropy loss (ablation) | TVGNN · 10 real-world datasets | AUC and Macro-F1 | Mixed |
| Use class-balanced focal loss instead of cross-entropy loss (ablation) | ChebyNet, BernNet, Gmixup, and GMT · 10 real-world datasets | AUC and Macro-F1 | No clear effect |
| Set CWGNN-RQ width to 4 (ablation) | RQGNN · MCF-7, SF-295, SN12C, and UACC257 | Macro-F1 | Helped |
| Set CWGNN-RQ depth to 6 (ablation) | RQGNN · MCF-7, SF-295, SN12C, and UACC257 | Macro-F1 | No clear effect |
Surprising findings
- Standard spectral GNNs (ChebyNet, BernNet) and graph classification models perform far below dedicated anomaly detectors, and class-balanced focal loss does not help ChebyNet, BernNet, Gmixup or GMT.
- Several one-class anomaly detectors (OCGIN, OCGTL, GLocalKD, HimNet) have AUC near or below 0.5 on some datasets, failing to beat generic GNN baselines.
Limitations
- Evaluation is limited to molecular anticancer screening datasets; other domains are only tested on small constructed datasets (COLORS-3, DBLP_v1).
- Hyperparameters such as beta, gamma, width and depth were tuned on the reported datasets, and baselines use default settings.
- Theoretical results are first-order perturbation bounds and the link to anomaly detection is supported mainly by empirical distribution observations.
Experimental setup
Datasets: MCF-7 MOLT-4 PC-3 SW-620 NCI-H23 OVCAR-8 P388 SF-295 SN12C UACC257 COLORS-3 DBLP_v1
Benchmarks: MCF-7 MOLT-4 PC-3 SW-620 NCI-H23 OVCAR-8 P388 SF-295 SN12C UACC257 COLORS-3 DBLP_v1
Metrics: AUC Macro-F1
Baselines: ChebyNet BernNet GMT Gmixup TVGNN OCGIN OCGTL GLocalKD HimNet iGAD
Builds on: ChebyNet BernNet CWGNN class-balanced loss focal loss
Closest papers by meaning
- Self-Discriminative Modeling for Anomalous Graph Detection (ICML 2025 · similarity 0.88)
- Dynamic Spectral Graph Anomaly Detection (AAAI 2025 · similarity 0.88)
- UniGAD: Unifying Multi-level Graph Anomaly Detection (NeurIPS 2024 · similarity 0.88)
- WaveNet: Tackling Non-stationary Graph Signals via Graph Spectral Wavelets (AAAI 2024 · similarity 0.87)
- Leveraging Diffusion Model as Pseudo-Anomalous Graph Generator for Graph-Level Anomaly Detection (ICML 2025 · similarity 0.87)
- Revisiting Graph Contrastive Learning on Anomaly Detection: A Structural Imbalance Perspective (AAAI 2025 · similarity 0.87)
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