# Bridging the Gap between Spatial and Spectral Domains: A Survey on Graph Neural Networks

arXiv: https://arxiv.org/abs/2002.11867 · HTML: https://mlsanity.com/paper/2002.11867/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2020.

## Built on by (most cited first, 15 of 15)

- [Model Stealing Attacks Against Inductive Graph Neural Networks](https://mlsanity.com/paper/2112.08331/) (2021)
- [Topological Relational Learning on Graphs](https://mlsanity.com/paper/2110.15529/) (2021)
- [Graph Neural Network-based EEG Classification: A Survey](https://mlsanity.com/paper/2310.02152/) (2023)
- [Bridging the Gap between Spatial and Spectral Domains: A Unified Framework for Graph Neural Networks](https://mlsanity.com/paper/2107.10234/) (2021)
- [Motif Prediction with Graph Neural Networks](https://mlsanity.com/paper/2106.00761/) (2021)
- [Neuromorphic Camera Denoising using Graph Neural Network-driven Transformers](https://mlsanity.com/paper/2112.09685/) (2021)
- [Graph Neural Networks for Multivariate Time Series Regression with Application to Seismic Data](https://mlsanity.com/paper/2201.00818/) (2022)
- [Neural Graph Databases](https://mlsanity.com/paper/2209.09732/) (2022)
- [Graph Neural Networks for Low-Energy Event Classification & Reconstruction in IceCube](https://mlsanity.com/paper/2209.03042/) (2022)
- [Two Trades is not Baffled: Condensing Graph via Crafting Rational Gradient Matching](https://mlsanity.com/paper/2402.04924/) (2024)
- [LON-GNN: Spectral GNNs with Learnable Orthonormal Basis](https://mlsanity.com/paper/2303.13750/) (2023)
- [Deep representation learning: Fundamentals, Perspectives, Applications, and Open Challenges](https://mlsanity.com/paper/2211.14732/) (2022)
- [GROWN+UP: A Graph Representation Of a Webpage Network Utilizing Pre-training](https://mlsanity.com/paper/2208.02252/) (2022)
- [Generative Graph Neural Networks for Link Prediction](https://mlsanity.com/paper/2301.00169/) (2022)
- [Self-Adaptive Graph Mixture of Models](https://mlsanity.com/paper/2511.13062/) (2025)

## Abstract (arXiv)

Deep learning's success has been widely recognized in a variety of machine learning tasks, including image classification, audio recognition, and natural language processing. As an extension of deep learning beyond these domains, graph neural networks (GNNs) are designed to handle the non-Euclidean graph-structure which is intractable to previous deep learning techniques. Existing GNNs are presented using various techniques, making direct comparison and cross-reference more complex. Although existing studies categorize GNNs into spatial-based and spectral-based techniques, there hasn't been a thorough examination of their relationship. To close this gap, this study presents a single framework that systematically incorporates most GNNs. We organize existing GNNs into spatial and spectral domains, as well as expose the connections within each domain. A review of spectral graph theory and approximation theory builds a strong relationship across the spatial and spectral domains in further investigation.