# Graph Signal Processing: History, Development, Impact, and Outlook

arXiv: https://arxiv.org/abs/2303.12211 · HTML: https://mlsanity.com/paper/2303.12211/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Mar 2023.

## Built on by (most cited first, 30 of 39)

- [Graph Deep Learning for Time Series Forecasting](https://mlsanity.com/paper/2310.15978/) (2023)
- [Video Anomaly Detection in 10 Years: A Survey and Outlook](https://mlsanity.com/paper/2405.19387/) (2024)
- [Two Trades is not Baffled: Condensing Graph via Crafting Rational Gradient Matching](https://mlsanity.com/paper/2402.04924/) (2024)
- [Continuous Product Graph Neural Networks](https://mlsanity.com/paper/2405.18877/) (2024)
- [Highly Efficient and Unsupervised Framework for Moving Object Detection in Satellite Videos](https://mlsanity.com/paper/2411.15895/) (2024)
- [Benchmarking Graph Neural Networks for Document Layout Analysis in Public Affairs](https://mlsanity.com/paper/2505.14699/) (2025)
- [Network Topology Inference with Sparsity and Laplacian Constraints](https://mlsanity.com/paper/2309.00960/) (2023)
- [Learning the Structure of Connection Graphs](https://mlsanity.com/paper/2510.11245/) (2025)
- [Binarized Simplicial Convolutional Neural Networks](https://mlsanity.com/paper/2405.04098/) (2024)
- [Correlating Time Series with Interpretable Convolutional Kernels](https://mlsanity.com/paper/2409.01362/) (2024)
- [Imputation of Time-varying Edge Flows in Graphs by Multilinear Kernel Regression and Manifold Learning](https://mlsanity.com/paper/2409.05135/) (2024)
- [Disentangling Neurodegeneration with Brain Age Gap Prediction Models: A Graph Signal Processing Perspective](https://mlsanity.com/paper/2510.12763/) (2025)
- [Time-Vertex Machine Learning for Optimal Sensor Placement in Temporal Graph Signals: Applications in Structural Health Monitoring](https://mlsanity.com/paper/2512.19309/) (2025)
- [Learning with Covariance Matrices: Principal Component Analysis Meets Learning with Graphs](https://mlsanity.com/paper/2609.10490/) (2026)
- [Spatiotemporal Forecasting Meets Efficiency: Causal Graph Process Neural Networks](https://mlsanity.com/paper/2405.18879/) (2024)
- [Graph Signal Adaptive Message Passing](https://mlsanity.com/paper/2410.17629/) (2024)
- [Deep spatio-temporal point processes: Advances and new directions](https://mlsanity.com/paper/2504.06364/) (2025)
- [Leveraging Low-rank Factorizations of Conditional Correlation Matrices in Graph Learning](https://mlsanity.com/paper/2506.10628/) (2025)
- [Directed Acyclic Graph Convolutional Networks](https://mlsanity.com/paper/2506.12218/) (2025)
- [Learning Time-Varying Graph Signals via Koopman](https://mlsanity.com/paper/2511.06493/) (2025)
- [Kernel-based Joint Multiple Graph Learning and Clustering of Graph Signals](https://mlsanity.com/paper/2310.19005/) (2023)
- [Adaptive Spatio-temporal Estimation on the Graph Edges via Line Graph Transformation](https://mlsanity.com/paper/2311.00656/) (2023)
- [Diffusion Maps for Signal Filtering in Graph Learning](https://mlsanity.com/paper/2312.14758/) (2023)
- [Fast Wrong-way Cycling Detection in CCTV Videos: Sparse Sampling is All You Need](https://mlsanity.com/paper/2405.07293/) (2024)
- [A Review of Graph-Powered Data Quality Applications for IoT Monitoring Sensor Networks](https://mlsanity.com/paper/2410.21006/) (2024)
- [Reconstruction of Graph Signals on Complex Manifolds with Kernel Methods](https://mlsanity.com/paper/2505.15202/) (2025)
- [Unrolling Dynamic Programming via Graph Filters](https://mlsanity.com/paper/2507.21705/) (2025)
- [Second-Order Tensorial Partial Differential Equations on Graphs](https://mlsanity.com/paper/2509.02015/) (2025)
- [From Federated Learning to X-Learning: Breaking the Barriers of Decentrality Through Random Walks](https://mlsanity.com/paper/2509.03709/) (2025)
- [Learning Time-Varying Graphs from Incomplete Graph Signals](https://mlsanity.com/paper/2510.17903/) (2025)

## Abstract (arXiv)

Graph signal processing (GSP) generalizes signal processing (SP) tasks to signals living on non-Euclidean domains whose structure can be captured by a weighted graph. Graphs are versatile, able to model irregular interactions, easy to interpret, and endowed with a corpus of mathematical results, rendering them natural candidates to serve as the basis for a theory of processing signals in more irregular domains. In this article, we provide an overview of the evolution of GSP, from its origins to the challenges ahead. The first half is devoted to reviewing the history of GSP and explaining how it gave rise to an encompassing framework that shares multiple similarities with SP. A key message is that GSP has been critical to develop novel and technically sound tools, theory, and algorithms that, by leveraging analogies with and the insights of digital SP, provide new ways to analyze, process, and learn from graph signals. In the second half, we shift focus to review the impact of GSP on other disciplines. First, we look at the use of GSP in data science problems, including graph learning and graph-based deep learning. Second, we discuss the impact of GSP on applications, including neuroscience and image and video processing. We conclude with a brief discussion of the emerging and future directions of GSP.