Research map / Graph learning / Knowledge and temporal graphs
Graph Structure Learning for Spatial-Temporal Imputation: Adapting to Node and Feature Scales
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Proposes GSLI, a multi-scale graph structure learning transformer-style framework that learns per-feature node-scale graphs and a feature-scale graph with prominence modeling to impute missing values in spatial-temporal data.
Problem
Spatial-temporal imputation with fixed spatial graphs assumes the same spatial relationships for all features across stations, ignoring feature heterogeneity and cross-feature spatial correlations.
Approach
Learns independent node-scale meta-graphs for each feature and a shared feature-scale meta-graph over features within nodes, both reweighted by learned prominence vectors, combined with cross-feature and cross-temporal self-attention.
Key results
- On DutchWind at 10% missing rate, GSLI achieves RMSE 0.410 and MAE 0.205, versus 0.437 / 0.229 for the next best GRIN.
- On CN at 10% missing rate, GSLI reaches RMSE 0.253 and MAE 0.120, compared with 0.370 / 0.205 for STD-GAE.
- Ablation on 10% missing values shows GSLI beats all nine variants on the four multi-feature datasets; removing feature-scale learning or GSL raises errors, and TemporalGCN is consistently worse than TemporalFeatureRL.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use GSLI instead of the strongest baseline | spatial-temporal imputation · DutchWind, BeijingMEO, LondonAQ, CN, Los, and LuohuTaxi, 10% missing | RMSE: 0.437 -> 0.410; 0.432 -> 0.399; 0.298 -> 0.272; 0.370 -> 0.253; 0.293 -> 0.263; 0.436 -> 0.410 | Helped |
| use GSLI instead of the strongest baseline | spatial-temporal imputation · DutchWind, BeijingMEO, LondonAQ, CN, Los, and LuohuTaxi, 10% missing | MAE: 0.217 -> 0.205; 0.208 -> 0.203; 0.182 -> 0.173; 0.179 -> 0.120; 0.188 -> 0.159; 0.301 -> 0.276 | Helped |
| add cross-temporal representation learning (ablation) | GSLI · DutchWind, BeijingMEO, LondonAQ, and CN, 10% missing | RMSE: 0.4221 -> 0.4101; 0.4308 -> 0.3986; 0.3515 -> 0.2720; 0.3723 -> 0.2534 | Helped |
| add cross-feature representation learning (ablation) | GSLI · DutchWind, BeijingMEO, LondonAQ, and CN, 10% missing | RMSE: 0.4140 -> 0.4101; 0.4160 -> 0.3986; 0.3079 -> 0.2720; 0.2609 -> 0.2534 | Mixed |
| add node-scale and feature-scale graph learning instead of canonical graph diffusion (ablation) | GSLI · DutchWind, BeijingMEO, LondonAQ, and CN, 10% missing | RMSE: 0.4147 -> 0.4101; 0.4018 -> 0.3986; 0.2825 -> 0.2720; 0.3100 -> 0.2534 | Helped |
| add node and feature prominence modeling (ablation) | GSLI · DutchWind, BeijingMEO, LondonAQ, and CN, 10% missing | RMSE: 0.4132 -> 0.4101; 0.4041 -> 0.3986; 0.2809 -> 0.2720; 0.2595 -> 0.2534 | Helped |
| add node-scale graph structure learning (ablation) | GSLI · DutchWind, BeijingMEO, LondonAQ, and CN, 10% missing | RMSE: 0.4130 -> 0.4101; 0.4015 -> 0.3986; 0.2845 -> 0.2720; 0.2631 -> 0.2534 | Helped |
| add feature-scale graph structure learning (ablation) | GSLI · DutchWind, BeijingMEO, LondonAQ, and CN, 10% missing | RMSE: 0.4213 -> 0.4101; 0.4083 -> 0.3986; 0.2966 -> 0.2720; 0.2932 -> 0.2534 | Helped |
| add graph structure learning rather than use only the given adjacency (ablation) | GSLI · DutchWind, BeijingMEO, LondonAQ, and CN, 10% missing | RMSE: 0.4218 -> 0.4101; 0.4090 -> 0.3986; 0.2990 -> 0.2720; 0.2962 -> 0.2534 | Helped |
| replace the given-graph-only TemporalGCN configuration with the fuller GSLI components (ablation) | GSLI · DutchWind, BeijingMEO, LondonAQ, and CN, 10% missing | RMSE: 0.4453 -> 0.4101; 0.4175 -> 0.3986; 0.3133 -> 0.2720; 0.2989 -> 0.2534 | Helped |
| replace the TemporalFeatrueRL configuration with the fuller GSLI components (ablation) | GSLI · DutchWind, BeijingMEO, LondonAQ, and CN, 10% missing | RMSE: 0.4223 -> 0.4101; 0.4111 -> 0.3986; 0.2926 -> 0.2720; 0.3053 -> 0.2534 | Helped |
Surprising findings
- Current spatial-temporal imputation methods do not significantly outperform multivariate time series imputation methods, which the authors attribute to imprecise given graphs.
- Different missing mechanisms (MCAR, MAR, MNAR) yield similar performance levels across methods.
Limitations
- Resource consumption is somewhat higher than the canonical graph diffusion convolution ablation.
- Results rely on the graph-building choices (thresholded Gaussian kernel) for datasets without adjacency matrices.
Experimental setup
Datasets: DutchWind BeijingMEO LondonAQ CN Los LuohuTaxi
Benchmarks: DutchWind BeijingMEO LondonAQ CN Los LuohuTaxi
Metrics: RMSE MAE
Baselines: CSDI TimesNet SAITS GPT4TS LRTC-TNN GRIN STD-GAE DAMR PriSTI PoGeVon ImputeFormer
Builds on: graph diffusion convolution GRIN Graph WaveNet CSDI PriSTI
Closest papers by meaning
- Learning from Highly Sparse Spatio-temporal Data (NeurIPS 2024 · similarity 0.91)
- RDPI: A Refine Diffusion Probability Generation Method for Spatiotemporal Data Imputation (AAAI 2025 · similarity 0.88)
- Fully-Connected Spatial-Temporal Graph for Multivariate Time-Series Data (AAAI 2024 · similarity 0.87)
- STD-PLM: Understanding Both Spatial and Temporal Properties of Spatial-Temporal Data with PLM (AAAI 2025 · similarity 0.86)
- Motif-aware Graph Neural Networks for Networked Time Series Imputation (AAAI 2025 · similarity 0.86)
- STRAP: Spatio-Temporal Pattern Retrieval for Out-of-Distribution Generalization (NeurIPS 2025 · similarity 0.86)
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