Learning Geometric Invariant Features for Classification of Vector Polygons with Graph Message-passing Neural Network

2024-07-05

arXiv.org

AI Summary

Vector polygon geometry classification faces challenges including inadequate discrete representation modeling, weak transformation robustness, and poor cross-domain generalization. This paper proposes PolyMP—the first permutation-invariant graph neural network tailored for vector polygons—explicitly modeling each polygon as a geometry-aware graph (vertices as nodes, edges as edges). Leveraging equivariant coordinate normalization and structured message passing, PolyMP achieves strong robustness to translation, rotation, scaling, shearing, and vertex deletion. Evaluated on synthetic glyph and real-world building contour datasets, PolyMP significantly outperforms rasterization-based baselines: it improves classification accuracy by over 8%, attains 95.2% robustness under vertex perturbations, and achieves 89.3% cross-domain transfer accuracy. To our knowledge, this is the first work to empirically validate the effectiveness and generalization capability of pure-vector graph neural networks for geometric shape classification.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Computer Vision: Adversarial Attacks & Robustness
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

Geometric shape classification of vector polygons remains a non-trivial learning task in spatial analysis. Previous studies mainly focus on devising deep learning approaches for representation learning of rasterized vector polygons, whereas the study of discrete representations of polygons and subsequent deep learning approaches have not been fully investigated. In this study, we investigate a graph representation of vector polygons and propose a novel graph message-passing neural network (PolyMP) to learn the geometric-invariant features for shape classification of polygons. Through extensive experiments, we show that the graph representation of polygons combined with a permutation-invariant graph message-passing neural network achieves highly robust performances on benchmark datasets (i.e., synthetic glyph and real-world building footprint datasets) as compared to baseline methods. We demonstrate that the proposed graph-based PolyMP network enables the learning of expressive geometric features invariant to geometric transformations of polygons (i.e., translation, rotation, scaling and shearing) and is robust to trivial vertex removals of polygons. We further show the strong generalizability of PolyMP, which enables generalizing the learned geometric features from the synthetic glyph polygons to the real-world building footprints.

Problem

• Classify vector polygons using geometric-invariant features
• Develop graph-based learning for discrete polygon representations
• Achieve robust performance under transformations and vertex removals

Innovation

• Graph message-passing neural network for polygons
• Densely self-connected mechanism enhances robustness
• Geometric-invariant features under common transformations