Research map / Graph learning / Knowledge and temporal graphs
Designing Specialized Two-Dimensional Graph Spectral Filters for Spatial-Temporal Graph Modeling
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Proposes STSGNN, which extends graph spectral filtering to a 2-D spatial-temporal domain via a 2-D discrete graph Fourier transform and learned bivariate Bernstein polynomial filters, followed by pyramidal gated convolutions, and reports state-of-the-art traffic and meteorological forecasting.
Problem
Spatial-temporal graph forecasting, where existing GNN-based models act as purely spatial low-pass filters and separate spatial from temporal modeling, failing to capture diverse node interactions with unified spatial-temporal dependencies.
Approach
Treats spatial and temporal graphs jointly by applying a 2-D DGFT over their normalized Laplacian spectra, then designs a 2-D filter via bivariate Bernstein polynomial approximation whose coefficients are generated adaptively from the input's spatial and temporal embeddings.
Key results
- STSGNN achieves average improvements of 4.1% MAE, 5.5% MAPE and 3.0% RMSE over the second-best method on traffic datasets.
- On meteorological datasets STSGNN improves MAE and RMSE by 3.2% and 2.7% over the second-best method.
- Ablation shows the variant using only low-pass filtering (V-OLP) is clearly worse than STSGNN, and V-OLP degrades with depth while STSGNN stays stable.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace low-pass-only filtering (V-OLP) with learned 2-D spectral filters (full STSGNN) (ablation) | STSGNN spatial-temporal filtering · PeMS04, PeMS08, KA-PM2.5 ablation | error (lower better) | Helped |
| Use only spatial graph spectral filtering (V-OSF) instead of joint 2-D filtering (ablation) | STSGNN · PeMS04, PeMS08, KA-PM2.5 ablation | error (lower better) | Helped |
| Use only temporal graph spectral filtering (V-OTF) instead of joint 2-D filtering (ablation) | STSGNN · PeMS04, PeMS08, KA-PM2.5 ablation | error (lower better) | Helped |
| Discard 2-D graph filtering operation (V-DSTF) (ablation) | STSGNN · PeMS04, PeMS08, KA-PM2.5 ablation | error (lower better) | Helped |
| Add pyramidal gated convolution module (vs discarding it, V-DPC) (ablation) | STSGNN · PeMS04, PeMS08, KA-PM2.5 ablation | error (lower better) | Helped |
| Filter over graph built from diverse node interactions instead of pattern-similarity spatial graph (V-SS) (ablation) | STSGNN · PeMS04, PeMS08, KA-PM2.5 ablation | error (lower better) | Helped |
| Increase network depth from low-pass-only (V-OLP) to deeper STSGNN ST blocks (ablation) | STSGNN vs V-OLP · PeMS04 depth analysis | error stability with depth | Mixed |
| Replace existing GNN-based and attention baselines with STSGNN across traffic and meteorological datasets | spatial-temporal forecasting · PeMS03/04/07/08, KA-UW/TEMP/PM2.5 | MAE: avg 4.1% MAE improvement on traffic, 3.2% on meteorological vs second best | Helped |
Surprising findings
- Learned 2-D filter coefficients closely match the shapes of the learned filter curves, supporting interpretability claims.
Limitations
- Computational cost of the 2-D filtering grows with P, Q and graph edge counts, which the authors acknowledge as high complexity.
- Evaluation limited to traffic and meteorological forecasting tasks.
Experimental setup
Datasets: PeMS03 PeMS04 PeMS07 PeMS08 KnowAir KA-UW KnowAir KA-TEMP KnowAir KA-PM2.5
Benchmarks: PeMS03 PeMS04 PeMS07 PEMS08 KA-UW KA-TEMP KA-PM2.5
Metrics: MAE RMSE MAPE
Baselines: VAR FC-LSTM STGCN STSGCN StemGNN MTGNN AGCRN STGODE STGNCDE GRETO ASTGCN GMAN
Builds on: ChebNet-style spectral graph convolution BernNet STGCN GMAN DSTAGNN
Closest papers by meaning
- Spatio-Spectral Graph Neural Networks (NeurIPS 2024 · similarity 0.92)
- Towards Dynamic Spatial-Temporal Graph Learning: A Decoupled Perspective (AAAI 2024 · similarity 0.89)
- HoloNets: Spectral Convolutions do extend to Directed Graphs (ICLR 2024 · similarity 0.88)
- Graph Neural Networks Are More Than Filters: Revisiting and Benchmarking from A Spectral Perspective (ICLR 2025 · similarity 0.88)
- SLOG: An Inductive Spectral Graph Neural Network Beyond Polynomial Filter (ICML 2024 · similarity 0.88)
- WaveNet: Tackling Non-stationary Graph Signals via Graph Spectral Wavelets (AAAI 2024 · similarity 0.88)
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