  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.
