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PolygonGNN: Representation Learning for Polygonal Geometries with Heterogeneous Visibility Graph

Dazhou Yu, Yuntong Hu, Yun Li, Liang Zhao

TL;DR

Multipolygon representation learning lags behind single-polygon methods by neglecting inner and inter-polygon relationships. The authors introduce PolygonGNN, which converts multipolygons into a heterogeneous visibility graph, uses a spanning-tree sampling strategy for efficiency, and employs a lossless five-tuple geometric representation to achieve rotation- and translation-invariance. A dedicated Multipolygon-GNN then performs two-hop message passing to capture hierarchical spatial patterns across polygon parts, producing discriminative embeddings. Across five datasets, the approach achieves state-of-the-art results and demonstrates robustness to perturbations, highlighting its practical value for GIS, urban planning, and related spatial analyses.

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

PolygonGNN: Representation Learning for Polygonal Geometries with Heterogeneous Visibility Graph

TL;DR

Multipolygon representation learning lags behind single-polygon methods by neglecting inner and inter-polygon relationships. The authors introduce PolygonGNN, which converts multipolygons into a heterogeneous visibility graph, uses a spanning-tree sampling strategy for efficiency, and employs a lossless five-tuple geometric representation to achieve rotation- and translation-invariance. A dedicated Multipolygon-GNN then performs two-hop message passing to capture hierarchical spatial patterns across polygon parts, producing discriminative embeddings. Across five datasets, the approach achieves state-of-the-art results and demonstrates robustness to perturbations, highlighting its practical value for GIS, urban planning, and related spatial analyses.

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}{}.
Paper Structure (28 sections, 5 theorems, 6 equations, 7 figures, 2 tables)

This paper contains 28 sections, 5 theorems, 6 equations, 7 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Polygon Representation Learning
  4. Graph Neural Networks for Multipolygons
  5. Problem Formulation
  6. Methodology
  7. Transforming Multipolygon to Heterogeneous Visibility Graph
  8. Heterogeneous Spanning Tree Sampling
  9. Heterogeneous Geometric Representation
  10. Multipolygon Graph Neural Network
  11. Experiment
  12. Experiment Setting
  13. Datasets
  14. Comparison Method
  15. Effectiveness Analysis
  16. ...and 13 more sections

Key Result

Theorem 4.1

Let $q$ be a multipolygon and $G(V,E, X, \phi)$ be the heterogeneous visibility graph derived from $q$, the transformation to the graph is invertible.

Figures (7)

  • Figure 1: Illustrations of building multipolygon patterns for (a) houses, (b) townhouses, and (c) commercial buildings.
  • Figure 2: Illustration of the proposed framework.
  • Figure 3: Message number comparison
  • Figure 4: Hyperparameter sensitivity
  • Figure 5: Visualization of learned embeddings in Building-S dataset after PCA dimensionality reduction.
  • ...and 2 more figures

Theorems & Definitions (7)

  • Definition 3.1
  • Definition 3.2
  • Theorem 4.1
  • Corollary 4.2
  • Lemma 4.3
  • Theorem 4.4
  • Theorem 4.5