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Poly2Vec: Polymorphic Fourier-Based Encoding of Geospatial Objects for GeoAI Applications
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Proposes Poly2Vec, a polymorphic encoder that maps points, polylines and polygons to a fixed-size embedding by fusing learned transforms of the magnitude and phase of their 2D continuous Fourier transform.
Problem
Existing geospatial encoders are object-specific (point, trajectory, or polygon encoders) or convert geometries to images or text, losing spatial relations such as topology, direction, and distance, which hurts GeoAI tasks that mix object types.
Approach
Compute closed-form 2D continuous Fourier transforms of points (Dirac deltas), line segments and triangles, sample frequencies on a geometric grid, and adaptively fuse the magnitude and phase through separate MLPs and a final MLP into one polymorphic geometry embedding.
Key results
- On topological classification, Poly2Vec reaches 0.955 accuracy on Singapore point-polyline versus 0.892 for the best baseline Theory, and up to 0.702 on polygon-polygon versus 0.602 for NUFTspec.
- In the RegionDCL pipeline, replacing the distance-biased term with Poly2Vec lowers population prediction MAE on Singapore from 5807.54 to 4957.58 and on New York from 5020.20 to 4602.75.
- Distance estimation MAE for point-point pairs on Singapore is 0.016 for Poly2Vec versus 0.065 for the best baseline Theory.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace RegionDCL object encodings and remove its distance-bias term using Poly2Vec | RegionDCL · Land use classification, Singapore and New York | L1, KL, and Cosine: Singapore L1: 0.498 -> 0.484; KL: 0.294 -> 0.278; Cosine: 0.879 -> 0.881. New York L1: 0.418 -> 0.397; KL: 0.229 -> 0.21 | Helped |
| Replace RegionDCL object encodings and remove its distance-bias term using Poly2Vec | RegionDCL · Population prediction, Singapore and New York | MAE, RMSE, and R^2: Singapore MAE: 5807.54 -> 4957.58; RMSE: 7942.74 -> 6874.47; R^2: 0.427 -> 0.561. New York MAE: 5020.20 -> 4602.75; RMSE | Helped |
| Remove the distance-bias term (ablation) | RegionDCL · Land use inference and population prediction | task performance | Hurt |
| Use only Fourier magnitude instead of learned fusion (ablation) | Poly2Vec · Point-polygon spatial reasoning tasks | task performance | Hurt |
| Use only Fourier phase instead of learned fusion (ablation) | Poly2Vec · Point-polygon spatial reasoning tasks | task performance | Mixed |
| Concatenate magnitude and phase without learned fusion (ablation) | Poly2Vec · Point-polygon spatial reasoning tasks | task performance | Helped |
| Learn frequency values rather than fixing geometrically sampled frequencies (ablation) | Poly2Vec · Point-polygon spatial reasoning tasks | task performance | No clear effect |
Surprising findings
- Learning the sampling frequencies instead of fixing a geometric grid did not yield significant improvements.
- T2Vec, a trajectory encoder, underperforms on directional classification due to grid discretization artifacts.
Limitations
- Limited to 2D geometries; extension to 3D is left for future work.
- Polygons are decomposed into triangles, and multipolygons are only mentioned as adaptable.
- Frequency sampling was fixed in the main experiments, with learned frequencies showing no benefit.
Experimental setup
Datasets: OpenStreetMap Singapore OpenStreetMap New York WorldPop population labels Singapore Master Plan 2019 land use NYC MapPLUTO
Benchmarks: topological relationship classification (Singapore, New York) directional relationship classification (Singapore, New York) distance estimation (Singapore, New York) land use inference population prediction
Metrics: accuracy precision recall F1 MSE MAE L1 KL divergence cosine similarity RMSE
Baselines: Direct Tile Wrap Grid Theory T2Vec ResNet1D NUFTspec RegionDCL
Builds on: NUFTspec RegionDCL Transformer positional encoding T2Vec
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