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Through the Dual-Prism: A Spectral Perspective on Graph Data Augmentation for Graph Classifications
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Proposes Dual-Prism (DP-Noise and DP-Mask), spectral graph augmentations that perturb only high-frequency Laplacian eigenvalues to preserve graph properties while diversifying graphs, evaluated for graph classification across supervised, semi-supervised, unsupervised and transfer settings.
Problem
Existing graph data augmentation methods distort important graph properties (e.g., diameter, connectivity) and make only localized structural changes, limiting their usefulness for GNN graph classification.
Approach
Use a spectral lens to find that low-frequency Laplacian eigenvalues govern key graph properties, so augmentation that perturbs only high-frequency eigenvalues (via additive noise or masking) and reconstructs the adjacency matrix can preserve properties while still producing diverse, structurally varied graphs.
Key results
- In supervised GIN experiments, DP-Noise reaches 61.67% on IMDB-MULTI versus 50.13% for the best prior baseline (S-Mixup), and 90.56% on NCI1 versus 80.02%.
- In unsupervised learning, DP-Mask reaches 79.47% on NCI1 and DP-Noise 79.69% versus GCL-SPAN at 71.43%, with DP methods surpassing baselines on five of seven datasets.
- In transfer learning, DP-Mask achieves 83.52% ROC-AUC on ClinTox, nearly 10 points above GraphCL (75.99%).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply DP-Noise augmentation rather than the strongest listed baseline | GIN graph classification · REDDIT-BINARY supervised | accuracy | Helped |
| Use DP-Noise augmentation rather than the strongest listed baseline | GIN graph classification · IMDB-MULTI supervised | accuracy | Helped |
| Use DP-Noise augmentation rather than the strongest listed baseline | semi-supervised graph classification with 10% labels · COLLAB | accuracy | Helped |
| Use DP-Noise augmentation rather than the strongest listed baseline | unsupervised graph classification · NCI1 | accuracy | Helped |
| Use DP-Mask rather than GraphCL pretraining augmentation | transfer learning graph classification · ClinTox | ROC-AUC | Helped |
| Perturb high-frequency rather than low-frequency eigenvalues (ablation) | DP-Noise on IMDB-BINARY · IMDB-BINARY | accuracy | Helped |
| Increase the standard deviation of noise in high-frequency components (ablation) | DP-Noise on IMDB-BINARY · IMDB-BINARY | accuracy | Helped |
| Increase frequency ratio for low-frequency components (ablation) | DP-Noise on IMDB-BINARY · IMDB-BINARY | accuracy | No clear effect |
| Increase frequency ratio beyond around 30% for high-frequency perturbation (ablation) | DP-Noise on IMDB-BINARY · IMDB-BINARY | accuracy | Hurt |
| Pair DP-Noise or DP-Mask with dropN (ablation) | DP-Noise and DP-Mask semi-supervised augmentation · Seven semi-supervised datasets | accuracy gain | Helped |
| Change the pairing augmentation method (ablation) | DP-Noise and DP-Mask semi-supervised augmentation · Seven semi-supervised datasets | accuracy gain | Mixed |
Surprising findings
- Perturbing high-frequency eigenvalues hurt accuracy less than perturbing low-frequency ones, and accuracy declined noticeably once the perturbed high-frequency ratio exceeded about 30%.
- DropEdge substantially altered graph properties (diameter, radius, periphery count) while DP-Noise kept them intact in the illustrated example.
Limitations
- Eigendecomposition and reconstruction scale as O(n^3), which is costly for large graphs.
- Uses the unnormalized Laplacian because normalized Laplacian reconstruction is intractable, a design choice that is motivated but not fully explored.
- Best augmentation partner and hyperparameters vary by dataset, so no single configuration dominates.
Experimental setup
Datasets: IMDB-BINARY IMDB-MULTI REDDIT-BINARY REDDIT-MULTI-5K REDDIT-MULTI-12K PROTEINS NCI1 ogbg-molhiv DD COLLAB GITHUB MUTAG
Benchmarks: IMDB-BINARY IMDB-MULTI REDDIT-BINARY REDDIT-MULTI-5K REDDIT-MULTI-12K PROTEINS NCI1 ogbg-molhiv DD COLLAB GITHUB MUTAG
Metrics: accuracy ROC-AUC
Baselines: DropEdge DropNode Subgraph M-Mixup SubMix G-Mixup S-Mixup Vanilla Aug. GAE Infomax GraphCL
Builds on: DropEdge GraphCL GCL-SPAN G-Mixup S-Mixup
Closest papers by meaning
- Data Augmentation for Graph Neural Networks (AAAI 2021 · similarity 0.91)
- Spectral Augmentation for Self-Supervised Learning on Graphs (ICLR 2023 · similarity 0.90)
- Spectral Graph Neural Networks are Incomplete on Graphs with a Simple Spectrum (NeurIPS 2025 · similarity 0.88)
- Graph Neural Networks Are More Than Filters: Revisiting and Benchmarking from A Spectral Perspective (ICLR 2025 · similarity 0.88)
- Community-Invariant Graph Contrastive Learning (ICML 2024 · similarity 0.88)
- Homomorphism Expressivity of Spectral Invariant Graph Neural Networks (ICLR 2025 · similarity 0.87)
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