Curvature‐Adaptive Embedding of Geographic Knowledge Graphs in Hyperbolic Space

Geographic Knowledge Graph Embedding (GKGE) maps the entities, relations, and attributes in a Geographic Knowledge Graph (GeoKG) into low‐dimensional vectors, supporting geographic intelligence tasks. However, most existing methods rely on Euclidean space, which struggles to model complex hierarchies (e.g., administrative district nesting) and spatial heterogeneity (e.g., uneven relationship density between urban and rural areas). To address these issues, we propose a curvature‐adaptive hyperbolic GKGE (CAH‐GKGE) method. Specifically, by leveraging the negative curvature of hyperbolic space, CAH‐GKGE not only effectively captures hierarchical structures but also dynamically adapts local curvature to reflect regional structural variations. To achieve this, it adopts a region‐guided subgraph sampling strategy to partition the GeoKG and employs meta‐learning to optimize curvature for each region, thereby enhancing structural representation and modeling spatial heterogeneity. Experiments on 13 GeoKG datasets demonstrate that CAH‐GKGE consistently outperforms competitive baselines across multiple evaluation metrics, validating its effectiveness. This study introduces a novel framework for modeling complex hierarchical structures in GeoKGs through curvature adaptation.