Geo2Vec: Shape- and Distance-Aware Neural Representation of Geospatial Entities

Abstract Spatial representation learning is fundamental to GeoAI applications, including urban analytics, as it encodes the shapes, locations, and spatial relationships (topological and distance-based) of geo-entities such as points, polylines, and polygons. Existing methods either target a single geo-entity type or, like Poly2Vec, decompose entities into simpler components to enable Fourier transformation, introducing high computational cost. Moreover, since the transformed space lacks geometric alignment, these methods rely on uniform, non-adaptive sampling, which blurs fine-grained features like edges and boundaries. To address these limitations, we introduce Geo2Vec, a novel method inspired by signed distance fields (SDF) that operates directly in the original space. Geo2Vec adaptively samples points and encodes their signed distances (positive outside, negative inside), capturing geometry without decomposition. A neural network trained to approximate the SDF produces compact, geometry-aware, and unified representations for all geo-entity types. Additionally, we propose a rotation-invariant positional encoding to model high-frequency spatial variations and construct a structured and robust embedding space for downstream GeoAI models. Empirical results show that Geo2Vec consistently outperforms existing methods in representing shape and location, capturing topological and distance relationships, and achieving greater efficiency in real-world GeoAI applications.