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Fully-Connected Spatial-Temporal Graph for Multivariate Time-Series Data
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Proposes FC-STGNN, which builds a fully-connected sensor graph across all timestamps with a temporal-distance decay matrix and applies moving-pooling GNN layers, to model spatial-temporal dependencies in multivariate time series for RUL prediction, HAR and sleep staging.
Problem
Existing GNN-based MTS methods model spatial and temporal dependencies separately and miss correlations between different sensors at different timestamps (DEDT), limiting representation learning.
Approach
Connect all sensors across all patches with dot-product edges weighted by a temporal decay matrix (delta^(t-r)), then apply graph convolution within moving windows over patches followed by temporal average pooling.
Key results
- On C-MAPSS FD001 the method reaches RMSE 11.62 vs. 12.58 for the second-best GCN (about 7.6% improvement).
- On UCI-HAR accuracy is 95.81% vs. 94.79% for GCN (about 1.02% improvement).
- On ISRUC-S3 accuracy is 80.87% vs. 79.31% for HierCorrPool (about 1.56% improvement).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use FC graph construction and graph convolution rather than separate per-patch graphs and convolutions (ablation) | FC-STGNN · C-MAPSS FD001 | RMSE: 12.58$\pm$0.22 -> 11.62$\pm$0.19 | Helped |
| Add the moving window and temporal pooling (ablation) | FC-STGNN · C-MAPSS FD001 | RMSE: 12.17$\pm$0.16 -> 11.62$\pm$0.19 | Helped |
| Add temporal pooling (ablation) | FC-STGNN · C-MAPSS FD001 | RMSE: 12.03$\pm$0.22 -> 11.62$\pm$0.19 | Helped |
| Add the decay matrix to the FC graph (ablation) | FC-STGNN · C-MAPSS FD001 | RMSE: 12.15$\pm$0.17 -> 11.62$\pm$0.19 | Helped |
| Add FC graph construction and convolution rather than separate per-patch graphs and convolutions (ablation) | FC-STGNN · UCI-HAR | Accuracy: 94.79$\pm$0.33 -> 95.81$\pm$0.24 | Helped |
| Add the moving window and temporal pooling (ablation) | FC-STGNN · UCI-HAR | Accuracy: 95.06$\pm$0.26 -> 95.81$\pm$0.24 | Helped |
| Add temporal pooling (ablation) | FC-STGNN · UCI-HAR | Accuracy: 95.53$\pm$0.30 -> 95.81$\pm$0.24 | Helped |
| Add the decay matrix to the FC graph (ablation) | FC-STGNN · UCI-HAR | Accuracy: 95.20$\pm$0.27 -> 95.81$\pm$0.24 | Helped |
| Add FC graph construction and convolution rather than separate per-patch graphs and convolutions (ablation) | FC-STGNN · ISRUC-S3 | MF1: 77.57$\pm$0.94 -> 78.79$\pm$0.55 | Helped |
| Add the moving window and temporal pooling (ablation) | FC-STGNN · ISRUC-S3 | MF1: 77.60$\pm$0.74 -> 78.79$\pm$0.55 | Helped |
| Add temporal pooling (ablation) | FC-STGNN · ISRUC-S3 | MF1: 77.42$\pm$0.80 -> 78.79$\pm$0.55 | Helped |
| Add the decay matrix to the FC graph (ablation) | FC-STGNN · ISRUC-S3 | MF1: 78.33$\pm$0.72 -> 78.79$\pm$0.55 | Helped |
Surprising findings
- Removing the FC graph convolution in the 'w/o FC GC' variant on C-MAPSS FD001 is the largest drop, while on FD002 the complete model does not beat MAGNN or HierCorrPool in score.
Limitations
- Gains on some C-MAPSS sub-datasets (e.g., FD002 RMSE and score) are not consistently best.
- Performance drops with too many parallel layers due to overfitting; window and decay hyperparameters require tuning per dataset.
Experimental setup
Datasets: C-MAPSS UCI-HAR ISRUC-S3
Benchmarks: C-MAPSS UCI-HAR ISRUC-S3
Metrics: RMSE Score Accuracy Macro-F1
Baselines: AConvLSTM DAGN InFormer AutoFormer GCN HAGCN HierCorrPool MAGNN
Builds on: MPNN positional encoding HierCorrPool GraphSleepNet
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