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

TL;DR

Poly2Vec introduces a polymorphic, Fourier-based encoding to unify 2D geospatial objects (points, polylines, polygons) into fixed-dimension embeddings. By decomposing the Fourier transform into magnitude and phase and learning task-adaptive fusion, it preserves shape, direction, and distance while remaining compatible with standard ML models. The approach outperforms object-specific baselines on spatial reasoning tasks (topology, direction, distance) and improves downstream GeoAI tasks such as population prediction and land use inference within an end-to-end pipeline. The work demonstrates the practicality of a unified spectral representation for heterogeneous geospatial data and outlines future extensions to higher dimensions and GeoAI foundations.

Abstract

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.

Figures (14)

• Figure 1: Visualization of the Fourier transform magnitude and phase of (a) road segment, (b) building, and (c) POI.
• Figure 2: Overview of Poly2Vec.
• Figure 3: Distance scatter plots of point-polygon pairs on Singapore dataset for different encoders.
• Figure 4: Ablation study for the point-polygon dataset.
• Figure 5: The effect of frequency sampling strategy on point-polygon pairs.

Theorems & Definitions (5)

• Definition 1: Geospatial Object
• Definition 2: Point
• Definition 3: Line Segment
• Definition 4: Polyline
• Definition 5: Polygon