PolygonGNN: Representation Learning for Polygonal Geometries with Heterogeneous Visibility Graph
This addresses the challenge of handling complex polygonal relationships in applications like shape coding and geographic analysis, though it appears incremental by extending graph-based methods to a specific domain.
The study tackled the problem of learning representations for polygonal geometries, especially multipolygons, by introducing a framework that incorporates a heterogeneous visibility graph to capture inner- and inter-polygonal relationships, resulting in a model that demonstrates effective representation capture on five datasets.
Polygon representation learning is essential for diverse applications, encompassing tasks such as shape coding, building pattern classification, and geographic question answering. While recent years have seen considerable advancements in this field, much of the focus has been on single polygons, overlooking the intricate inner- and inter-polygonal relationships inherent in multipolygons. To address this gap, our study introduces a comprehensive framework specifically designed for learning representations of polygonal geometries, particularly multipolygons. Central to our approach is the incorporation of a heterogeneous visibility graph, which seamlessly integrates both inner- and inter-polygonal relationships. To enhance computational efficiency and minimize graph redundancy, we implement a heterogeneous spanning tree sampling method. Additionally, we devise a rotation-translation invariant geometric representation, ensuring broader applicability across diverse scenarios. Finally, we introduce Multipolygon-GNN, a novel model tailored to leverage the spatial and semantic heterogeneity inherent in the visibility graph. Experiments on five real-world and synthetic datasets demonstrate its ability to capture informative representations for polygonal geometries. Code and data are available at \href{https://github.com/dyu62/PolyGNN}{$github.com/dyu62/PolyGNN$}.