PolygonGNN: Representation Learning for Polygonal Geometries with Heterogeneous Visibility Graph

TL;DR

PolygonGNN introduces a novel framework for learning multipolygon representations using a heterogeneous visibility graph and a specialized GNN model, improving understanding of complex geometric relationships.

Contribution

The paper presents a comprehensive multipolygon representation learning framework with a heterogeneous visibility graph and a new GNN model, addressing inner- and inter-polygonal relationships.

Findings

Effective in capturing geometric and semantic features

Performs well on real-world and synthetic datasets

Enhances multipolygon analysis accuracy

Abstract

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}{$github.com/dyu62/PolyGNN$}.