# Graph signal processing for machine learning: A review and new perspectives

arXiv: https://arxiv.org/abs/2007.16061 · HTML: https://mlsanity.com/paper/2007.16061/

## Key facts

- Cited by 73 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jul 2020.

## Built on by (most cited first, 30 of 73)

- [Specformer: Spectral Graph Neural Networks Meet Transformers](https://mlsanity.com/paper/2303.01028/) (2023)
- [Breaking the Limit of Graph Neural Networks by Improving the Assortativity of Graphs with Local Mixing Patterns](https://mlsanity.com/paper/2106.06586/) (2021)
- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [How Powerful is Graph Convolution for Recommendation?](https://mlsanity.com/paper/2108.07567/) (2021)
- [Interpretable Stability Bounds for Spectral Graph Filters](https://mlsanity.com/paper/2102.09587/) (2021)
- [A Survey on Spectral Graph Neural Networks](https://mlsanity.com/paper/2302.05631/) (2023)
- [Graph Structural Attack by Perturbing Spectral Distance](https://mlsanity.com/paper/2111.00684/) (2021)
- [Combinatorial Complexes: Bridging the Gap Between Cell Complexes and Hypergraphs](https://mlsanity.com/paper/2312.09504/) (2023)
- [Modeling Ideological Salience and Framing in Polarized Online Groups with Graph Neural Networks and Structured Sparsity](https://mlsanity.com/paper/2104.08829/) (2021)
- [On Manipulating Signals of User-Item Graph: A Jacobi Polynomial-based Graph Collaborative Filtering](https://mlsanity.com/paper/2306.03624/) (2023)
- [Fairness-Aware Graph Filter Design](https://mlsanity.com/paper/2303.11459/) (2023)
- [Redesigning graph filter-based GNNs to relax the homophily assumption](https://mlsanity.com/paper/2409.08676/) (2024)
- [Learning Sheaf Laplacian Optimizing Restriction Maps](https://mlsanity.com/paper/2501.19207/) (2025)
- [Bures-Wasserstein Means of Graphs](https://mlsanity.com/paper/2305.19738/) (2023)
- [Convolutional Learning on Directed Acyclic Graphs](https://mlsanity.com/paper/2405.03056/) (2024)
- [A Comprehensive Benchmark on Spectral GNNs: The Impact on Efficiency, Memory, and Effectiveness](https://mlsanity.com/paper/2406.09675/) (2024)
- [On the Stability of Low Pass Graph Filter With a Large Number of Edge Rewires](https://mlsanity.com/paper/2110.07234/) (2021)
- [Representing Edge Flows on Graphs via Sparse Cell Complexes](https://mlsanity.com/paper/2309.01632/) (2023)
- [Laplacian Constrained Precision Matrix Estimation: Existence and High Dimensional Consistency](https://mlsanity.com/paper/2111.00590/) (2021)
- [Graph Neural Networks with Parallel Neighborhood Aggregations for Graph Classification](https://mlsanity.com/paper/2111.11482/) (2021)
- [Graph Normalized-LMP Algorithm for Signal Estimation Under Impulsive Noise](https://mlsanity.com/paper/2203.00320/) (2022)
- [Complex-Value Spatio-temporal Graph Convolutional Neural Networks and its Applications to Electric Power Systems AI](https://mlsanity.com/paper/2208.08485/) (2022)
- [Graph Federated Learning for CIoT Devices in Smart Home Applications](https://mlsanity.com/paper/2212.14395/) (2022)
- [Graph Classification Gaussian Processes via Spectral Features](https://mlsanity.com/paper/2306.03770/) (2023)
- [DoFlow: Flow-based Generative Models for Interventional and Counterfactual Forecasting on Time Series](https://mlsanity.com/paper/2511.02137/) (2025)
- [TabGSL: Graph Structure Learning for Tabular Data Prediction](https://mlsanity.com/paper/2305.15843/) (2023)
- [Frequency-aware Graph Signal Processing for Collaborative Filtering](https://mlsanity.com/paper/2402.08426/) (2024)
- [Spectral GNN via Two-dimensional (2-D) Graph Convolution](https://mlsanity.com/paper/2404.04559/) (2024)
- [LLM Online Spatial-temporal Signal Reconstruction Under Noise](https://mlsanity.com/paper/2411.15764/) (2024)
- [A Few Moments Please: Scalable Graphon Learning via Moment Matching](https://mlsanity.com/paper/2506.04206/) (2025)

## Abstract (arXiv)

The effective representation, processing, analysis, and visualization of large-scale structured data, especially those related to complex domains such as networks and graphs, are one of the key questions in modern machine learning. Graph signal processing (GSP), a vibrant branch of signal processing models and algorithms that aims at handling data supported on graphs, opens new paths of research to address this challenge. In this article, we review a few important contributions made by GSP concepts and tools, such as graph filters and transforms, to the development of novel machine learning algorithms. In particular, our discussion focuses on the following three aspects: exploiting data structure and relational priors, improving data and computational efficiency, and enhancing model interpretability. Furthermore, we provide new perspectives on future development of GSP techniques that may serve as a bridge between applied mathematics and signal processing on one side, and machine learning and network science on the other. Cross-fertilization across these different disciplines may help unlock the numerous challenges of complex data analysis in the modern age.