# Poly2Vec: Polymorphic Fourier-Based Encoding of Geospatial Objects for GeoAI Applications

arXiv: https://arxiv.org/abs/2408.14806 · HTML: https://mlsanity.com/paper/2408.14806/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 42 references that are in the map.
- First posted on arXiv 27 Aug 2024.

## Builds on (most cited first, 24 of 24)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [VoxelNet: End-to-End Learning for Point Cloud Based 3D Object Detection](https://mlsanity.com/paper/1711.06396/) (2017)
- [Presence-Only Geographical Priors for Fine-Grained Image Classification](https://mlsanity.com/paper/1906.05272/) (2019)
- [Learning to Navigate in Cities Without a Map](https://mlsanity.com/paper/1804.00168/) (2018)
- [Multi-Scale Representation Learning for Spatial Feature Distributions using Grid Cells](https://mlsanity.com/paper/2003.00824/) (2020)
- [On the Opportunities and Challenges of Foundation Models for Geospatial Artificial Intelligence](https://mlsanity.com/paper/2304.06798/) (2023)
- [LSTM-TrajGAN: A Deep Learning Approach to Trajectory Privacy Protection](https://mlsanity.com/paper/2006.10521/) (2020)
- [Reconstructing continuous distributions of 3D protein structure from cryo-EM images](https://mlsanity.com/paper/1909.05215/) (2019)
- [MobTCast: Leveraging Auxiliary Trajectory Forecasting for Human Mobility Prediction](https://mlsanity.com/paper/2110.01401/) (2021)
- [Geo-Aware Networks for Fine-Grained Recognition](https://mlsanity.com/paper/1906.01737/) (2019)
- [Improving Image Classification with Location Context](https://mlsanity.com/paper/1505.03873/) (2015)
- [Multi-Graph Fusion Networks for Urban Region Embedding](https://mlsanity.com/paper/2201.09760/) (2022)
- [ERNIE-GeoL: A Geography-and-Language Pre-trained Model and its Applications in Baidu Maps](https://mlsanity.com/paper/2203.09127/) (2022)
- [Towards General-Purpose Representation Learning of Polygonal Geometries](https://mlsanity.com/paper/2209.15458/) (2022)
- [City Foundation Models for Learning General Purpose Representations from OpenStreetMap](https://mlsanity.com/paper/2310.00583/) (2023)
- [Template-Based Question Answering over Linked Geospatial Data](https://mlsanity.com/paper/2007.07060/) (2020)
- [PolygonGNN: Representation Learning for Polygonal Geometries with Heterogeneous Visibility Graph](https://mlsanity.com/paper/2407.00742/) (2024)
- [Deep Learning for Classification Tasks on Geospatial Vector Polygons](https://mlsanity.com/paper/1806.03857/) (2018)
- [Continuous Multiagent Control using Collective Behavior Entropy for Large-Scale Home Energy Management](https://mlsanity.com/paper/2005.10000/) (2020)
- [DDSL: Deep Differentiable Simplex Layer for Learning Geometric Signals](https://mlsanity.com/paper/1901.11082/) (2019)
- [Convolutional Neural Networks on non-uniform geometrical signals using Euclidean spectral transformation](https://mlsanity.com/paper/1901.02070/) (2019)
- [Three-dimensional Geospatial Interlinking with JedAI-spatial](https://mlsanity.com/paper/2205.01905/) (2022)

## Built on by (most cited first, 13 of 13)

- [Geo2Vec: Shape- and Distance-Aware Neural Representation of Geospatial Entities](https://mlsanity.com/paper/2508.19305/) (2025)
- [Towards Generative Location Awareness for Disaster Response: A Probabilistic Cross-view Geolocalization Approach](https://mlsanity.com/paper/2512.20056/) (2025)
- [S2Vec: Self-Supervised Geospatial Embeddings for the Built Environment](https://mlsanity.com/paper/2504.16942/) (2025)
- [Mobility-Embedded POIs: Learning What A Place Is and How It Is Used from Human Movement](https://mlsanity.com/paper/2601.21149/) (2026)
- [TerraDiT-Omega: Unified Spatial Control for Satellite Image Synthesis with Any Geospatial Primitive](https://mlsanity.com/paper/2606.31029/) (2026)
- [Spatial Representation Learning Beyond Pixels: Unifying Raster Data and Vector Semantics for Human-Centric Geospatial Foundation Models](https://mlsanity.com/paper/2606.02374/) (2026)
- [POIFormer: A Transformer-Based Framework for Accurate and Scalable Point-of-Interest Attribution](https://mlsanity.com/paper/2507.09137/) (2025)
- [Natural Language Interfaces for Spatial and Temporal Databases: A Comprehensive Overview of Methods, Taxonomy, and Future Directions](https://mlsanity.com/paper/2603.23375/) (2026)
- [TrajGANR: Trajectory-Centric Urban Multimodal Learning via Geospatially Aligned Neural Representations](https://mlsanity.com/paper/2605.06990/) (2026)
- [NARA: Anchor-Conditioned Representation Learning for Heterogeneous Vector Geoentities](https://mlsanity.com/paper/2605.12276/) (2026)
- [Automated Quality Assessment of Geospatial Vector Data: A GeoAI Approach using Spatial Representation Learning](https://mlsanity.com/paper/2606.28390/) (2026)
- [Airfoil2Vec: Spectral Geometry-Conditioned Neural Surrogate Models for Airfoil Aerodynamics and a Downforce-Generating CFD Dataset](https://mlsanity.com/paper/2609.38213/) (2026)
- [Geospatial Vector Geometry as a Native Spatial Modality for Vision-Language Models](https://mlsanity.com/paper/2610.16769/) (2026)

## Abstract (arXiv)

Encoding geospatial objects is fundamental for geospatial artificial intelligence (GeoAI) applications, which leverage machine learning (ML) models to analyze spatial information. Common approaches transform each object into known formats, like image and text, for compatibility with ML models. However, this process often discards crucial spatial information, such as the object's position relative to the entire space, reducing downstream task effectiveness. Alternative encoding methods that preserve some spatial properties are often devised for specific data objects (e.g., point encoders), making them unsuitable for tasks that involve different data types (i.e., points, polylines, and polygons). To this end, we propose Poly2Vec, a polymorphic Fourier-based encoding approach that unifies the representation of geospatial objects, while preserving the essential spatial properties. Poly2Vec incorporates a learned fusion module that adaptively integrates the magnitude and phase of the Fourier transform for different tasks and geometries. We evaluate Poly2Vec on five diverse tasks, organized into two categories. The first empirically demonstrates that Poly2Vec consistently outperforms object-specific baselines in preserving three key spatial relationships: topology, direction, and distance. The second shows that integrating Poly2Vec into a state-of-the-art GeoAI workflow improves the performance in two popular tasks: population prediction and land use inference.