PolygonGNN: Representation Learning for Polygonal Geometries with Heterogeneous Visibility Graph

2024-06-30

Knowledge Discovery and Data Mining

AI Summary

Existing works predominantly focus on single-polygon representations, neglecting internal structural properties and geometric dependencies among polygon collections. This paper introduces Multipolygon-GNN—the first end-to-end graph neural network framework designed for multi-part polygonal assemblies. To address these limitations, we: (i) construct a heterogeneous visibility graph that jointly encodes intra- and inter-polygon topological and visibility relationships; (ii) propose a heterogeneous spanning-tree sampling strategy coupled with rotation- and translation-invariant geometric encoding to explicitly capture rigid-body-invariant geometric features; and (iii) jointly optimize graph structure learning and representation learning. Evaluated on five real-world and synthetic datasets, our method significantly improves shape encoding fidelity, architectural pattern classification accuracy, and geospatial question-answering performance. The code and datasets are publicly available.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Computer Vision: Multi-modal Vision
• Machine Learning: Multi-instance/Multi-view Learning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG

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

Problem

• Learning representations for complex multipolygon geometries
• Modeling inner- and inter-polygonal relationships via visibility graphs
• Improving computational efficiency in polygonal geometry analysis

Innovation

• Heterogeneous visibility graph integrates polygonal relationships
• Spanning tree sampling reduces graph redundancy
• Rotation-translation invariant representation enhances applicability