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

arXiv: https://arxiv.org/abs/2407.04334 · HTML: https://mlsanity.com/paper/2407.04334/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 53 references that are in the map.
- First posted on arXiv 5 Jul 2024.

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
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- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [Conditional Image Synthesis With Auxiliary Classifier GANs](https://mlsanity.com/paper/1610.09585/) (2016)
- [RefineNet: Multi-Path Refinement Networks for High-Resolution Semantic Segmentation](https://mlsanity.com/paper/1611.06612/) (2016)
- [Rethinking Network Design and Local Geometry in Point Cloud: A Simple Residual MLP Framework](https://mlsanity.com/paper/2202.07123/) (2022)
- [A Neural Representation of Sketch Drawings](https://mlsanity.com/paper/1704.03477/) (2017)
- [DeepSVG: A Hierarchical Generative Network for Vector Graphics Animation](https://mlsanity.com/paper/2007.11301/) (2020)
- [A Learned Representation for Scalable Vector Graphics](https://mlsanity.com/paper/1904.02632/) (2019)
- [Towards General-Purpose Representation Learning of Polygonal Geometries](https://mlsanity.com/paper/2209.15458/) (2022)
- [Logo Synthesis and Manipulation with Clustered Generative Adversarial Networks](https://mlsanity.com/paper/1712.04407/) (2017)
- [Deep Learning for Classification Tasks on Geospatial Vector Polygons](https://mlsanity.com/paper/1806.03857/) (2018)
- [Towards Efficient Point Cloud Graph Neural Networks Through Architectural Simplification](https://mlsanity.com/paper/2108.06317/) (2021)
- [LoGAN: Generating Logos with a Generative Adversarial Neural Network Conditioned on color](https://mlsanity.com/paper/1810.10395/) (2018)

## Abstract (arXiv)

Geometric shape classification of vector polygons remains a challenging task in spatial analysis. Previous studies have primarily focused on deep learning approaches for rasterized vector polygons, while the study of discrete polygon representations and corresponding learning methods remains underexplored. In this study, we investigate a graph-based representation of vector polygons and propose a simple graph message-passing framework, PolyMP, along with its densely self-connected variant, PolyMP-DSC, to learn more expressive and robust latent representations of polygons. This framework hierarchically captures self-looped graph information and learns geometric-invariant features for polygon shape classification. Through extensive experiments, we demonstrate that combining a permutation-invariant graph message-passing neural network with a densely self-connected mechanism achieves robust performance on benchmark datasets, including synthetic glyphs and real-world building footprints, outperforming several baseline methods. Our findings indicate that PolyMP and PolyMP-DSC effectively capture expressive geometric features that remain invariant under common transformations, such as translation, rotation, scaling, and shearing, while also being robust to trivial vertex removals. Furthermore, we highlight the strong generalization ability of the proposed approach, enabling the transfer of learned geometric features from synthetic glyph polygons to real-world building footprints.