# Non-Euclidean Spatial Graph Neural Network

arXiv: https://arxiv.org/abs/2312.10808 · HTML: https://mlsanity.com/paper/2312.10808/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 52 references that are in the map.
- First posted on arXiv 17 Dec 2023.

## Builds on (most cited first, 21 of 21)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Multi-view Convolutional Neural Networks for 3D Shape Recognition](https://mlsanity.com/paper/1505.00880/) (2015)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [Learning Convolutional Neural Networks for Graphs](https://mlsanity.com/paper/1605.05273/) (2016)
- [PPFNet: Global Context Aware Local Features for Robust 3D Point Matching](https://mlsanity.com/paper/1802.02669/) (2018)
- [Deep Functional Maps: Structured Prediction for Dense Shape Correspondence](https://mlsanity.com/paper/1704.08686/) (2017)
- [SyncSpecCNN: Synchronized Spectral CNN for 3D Shape Segmentation](https://mlsanity.com/paper/1612.00606/) (2016)
- [Deep Graph Representation Learning and Optimization for Influence Maximization](https://mlsanity.com/paper/2305.02200/) (2023)
- [Deep Generative Model for Periodic Graphs](https://mlsanity.com/paper/2201.11932/) (2022)
- [An Invertible Graph Diffusion Neural Network for Source Localization](https://mlsanity.com/paper/2206.09214/) (2022)
- [Curriculum Learning for Graph Neural Networks: Which Edges Should We Learn First](https://mlsanity.com/paper/2310.18735/) (2023)
- [Random Spatial Network Models with Core-Periphery Structure](https://mlsanity.com/paper/1808.06544/) (2018)
- [Approximation Bounds for Interpolation and Normals on Triangulated Surfaces and Manifolds](https://mlsanity.com/paper/1911.03424/) (2019)

## Abstract (arXiv)

Spatial networks are networks whose graph topology is constrained by their embedded spatial space. Understanding the coupled spatial-graph properties is crucial for extracting powerful representations from spatial networks. Therefore, merely combining individual spatial and network representations cannot reveal the underlying interaction mechanism of spatial networks. Besides, existing spatial network representation learning methods can only consider networks embedded in Euclidean space, and can not well exploit the rich geometric information carried by irregular and non-uniform non-Euclidean space. In order to address this issue, in this paper we propose a novel generic framework to learn the representation of spatial networks that are embedded in non-Euclidean manifold space. Specifically, a novel message-passing-based neural network is proposed to combine graph topology and spatial geometry, where spatial geometry is extracted as messages on the edges. We theoretically guarantee that the learned representations are provably invariant to important symmetries such as rotation or translation, and simultaneously maintain sufficient ability in distinguishing different geometric structures. The strength of our proposed method is demonstrated through extensive experiments on both synthetic and real-world datasets.