# Graph Signal Processing: Overview, Challenges and Applications

arXiv: https://arxiv.org/abs/1712.00468 · HTML: https://mlsanity.com/paper/1712.00468/

## Key facts

- Cited by 413 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Dec 2017.

## Built on by (most cited first, 30 of 413)

- [Sign and Basis Invariant Networks for Spectral Graph Representation Learning](https://mlsanity.com/paper/2202.13013/) (2022)
- [Graph Learning: A Survey](https://mlsanity.com/paper/2105.00696/) (2021)
- [MagNet: A Neural Network for Directed Graphs](https://mlsanity.com/paper/2102.11391/) (2021)
- [Specformer: Spectral Graph Neural Networks Meet Transformers](https://mlsanity.com/paper/2303.01028/) (2023)
- [Video Summarization Using Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.06072/) (2021)
- [Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond](https://mlsanity.com/paper/2101.05510/) (2021)
- [Benchmarking and Analyzing Point Cloud Classification under Corruptions](https://mlsanity.com/paper/2202.03377/) (2022)
- [A Survey of Graph Neural Networks in Real world: Imbalance, Noise, Privacy and OOD Challenges](https://mlsanity.com/paper/2403.04468/) (2024)
- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Federated Graph Neural Networks: Overview, Techniques and Challenges](https://mlsanity.com/paper/2202.07256/) (2022)
- [Transferability Properties of Graph Neural Networks](https://mlsanity.com/paper/2112.04629/) (2021)
- [Revisiting Graph Contrastive Learning from the Perspective of Graph Spectrum](https://mlsanity.com/paper/2210.02330/) (2022)
- [Simplicial Convolutional Neural Networks](https://mlsanity.com/paper/2110.02585/) (2021)
- [Taming Local Effects in Graph-based Spatiotemporal Forecasting](https://mlsanity.com/paper/2302.04071/) (2023)
- [Bag of Tricks for Training Deeper Graph Neural Networks: A Comprehensive Benchmark Study](https://mlsanity.com/paper/2108.10521/) (2021)
- [Spectrally Pruned Gaussian Fields with Neural Compensation](https://mlsanity.com/paper/2405.00676/) (2024)
- [Modeling Multivariate Biosignals With Graph Neural Networks and Structured State Space Models](https://mlsanity.com/paper/2211.11176/) (2022)
- [Interpretable Stability Bounds for Spectral Graph Filters](https://mlsanity.com/paper/2102.09587/) (2021)
- [Moving Object Detection for Event-based vision using Graph Spectral Clustering](https://mlsanity.com/paper/2109.14979/) (2021)
- [RU-Net: Regularized Unrolling Network for Scene Graph Generation](https://mlsanity.com/paper/2205.01297/) (2022)
- [Learning to Learn Graph Topologies](https://mlsanity.com/paper/2110.09807/) (2021)
- [A Survey on Spectral Graph Neural Networks](https://mlsanity.com/paper/2302.05631/) (2023)
- [Graph Deep Learning for Time Series Forecasting](https://mlsanity.com/paper/2310.15978/) (2023)
- [Graph Neural Networks Based Detection of Stealth False Data Injection Attacks in Smart Grids](https://mlsanity.com/paper/2104.02012/) (2021)
- [Spatio-temporal graph neural networks for multi-site PV power forecasting](https://mlsanity.com/paper/2107.13875/) (2021)
- [Make Heterophily Graphs Better Fit GNN: A Graph Rewiring Approach](https://mlsanity.com/paper/2209.08264/) (2022)
- [Modularity-Aware Graph Autoencoders for Joint Community Detection and Link Prediction](https://mlsanity.com/paper/2202.00961/) (2022)
- [Sparse Graph Learning from Spatiotemporal Time Series](https://mlsanity.com/paper/2205.13492/) (2022)
- [Training Robust Graph Neural Networks with Topology Adaptive Edge Dropping](https://mlsanity.com/paper/2106.02892/) (2021)
- [coVariance Neural Networks](https://mlsanity.com/paper/2205.15856/) (2022)

## Abstract (arXiv)

Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal processing. We then summarize recent developments in developing basic GSP tools, including methods for sampling, filtering or graph learning. Next, we review progress in several application areas using GSP, including processing and analysis of sensor network data, biological data, and applications to image processing and machine learning. We finish by providing a brief historical perspective to highlight how concepts recently developed in GSP build on top of prior research in other areas.