# Graph Filters for Signal Processing and Machine Learning on Graphs

arXiv: https://arxiv.org/abs/2211.08854 · HTML: https://mlsanity.com/paper/2211.08854/

## Key facts

- Cited by 53 papers in the map (data through 14 Oct 2026).
- Builds on 156 of its 370 references that are in the map.
- First posted on arXiv 16 Nov 2022.

## Builds on (most cited first, 30 of 156)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2002.02126/) (2020)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Learning Lane Graph Representations for Motion Forecasting](https://mlsanity.com/paper/2007.13732/) (2020)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)
- [Pose2Mesh: Graph Convolutional Network for 3D Human Pose and Mesh Recovery from a 2D Human Pose](https://mlsanity.com/paper/2008.09047/) (2020)
- [CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters](https://mlsanity.com/paper/1705.07664/) (2017)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [How Powerful are Spectral Graph Neural Networks](https://mlsanity.com/paper/2205.11172/) (2022)
- [How to learn a graph from smooth signals](https://mlsanity.com/paper/1601.02513/) (2016)
- [A Survey of Graph Neural Networks for Recommender Systems: Challenges, Methods, and Directions](https://mlsanity.com/paper/2109.12843/) (2021)
- [Interpreting and Unifying Graph Neural Networks with An Optimization Framework](https://mlsanity.com/paper/2101.11859/) (2021)
- [ETA Prediction with Graph Neural Networks in Google Maps](https://mlsanity.com/paper/2108.11482/) (2021)
- [Stability Properties of Graph Neural Networks](https://mlsanity.com/paper/1905.04497/) (2019)
- [Weisfeiler and Leman go Machine Learning: The Story so far](https://mlsanity.com/paper/2112.09992/) (2021)
- [Revisiting Graph based Collaborative Filtering: A Linear Residual Graph Convolutional Network Approach](https://mlsanity.com/paper/2001.10167/) (2020)

## Built on by (most cited first, 30 of 53)

- [Graph Neural Networks with Learnable and Optimal Polynomial Bases](https://mlsanity.com/paper/2302.12432/) (2023)
- [Improving Protein Optimization with Smoothed Fitness Landscapes](https://mlsanity.com/paper/2307.00494/) (2023)
- [Cross-Contrastive Clustering for Multimodal Attributed Graphs with Dual Graph Filtering](https://mlsanity.com/paper/2511.20030/) (2025)
- [Spatiotemporal Covariance Neural Networks](https://mlsanity.com/paper/2409.10068/) (2024)
- [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)
- [Graph-Aware Diffusion for Signal Generation](https://mlsanity.com/paper/2510.05036/) (2025)
- [Sparse Covariance Neural Networks](https://mlsanity.com/paper/2410.01669/) (2024)
- [Fair CoVariance Neural Networks](https://mlsanity.com/paper/2409.08558/) (2024)
- [Recovering Missing Node Features with Local Structure-based Embeddings](https://mlsanity.com/paper/2309.09068/) (2023)
- [Topological Dictionary Learning](https://mlsanity.com/paper/2503.11470/) (2025)
- [Covariance Density Neural Networks](https://mlsanity.com/paper/2505.11139/) (2025)
- [Disentangling Neurodegeneration with Brain Age Gap Prediction Models: A Graph Signal Processing Perspective](https://mlsanity.com/paper/2510.12763/) (2025)
- [KrawtchoukNet: A Unified GNN Solution for Heterophily and Over-smoothing with Adaptive Bounded Polynomials](https://mlsanity.com/paper/2511.15327/) (2025)
- [Fairness-aware Optimal Graph Filter Design](https://mlsanity.com/paper/2310.14432/) (2023)
- [On the Trade-Off between Stability and Representational Capacity in Graph Neural Networks](https://mlsanity.com/paper/2312.02372/) (2023)
- [Online Learning Of Expanding Graphs](https://mlsanity.com/paper/2409.08660/) (2024)
- [Training-free Adjustable Polynomial Graph Filtering for Ultra-fast Multimodal Recommendation](https://mlsanity.com/paper/2503.04406/) (2025)
- [Topological Adaptive Least Mean Squares Algorithms over Simplicial Complexes](https://mlsanity.com/paper/2505.23160/) (2025)
- [GKNet: Graph Kalman Filtering and Model Inference via Model-based Deep Learning](https://mlsanity.com/paper/2506.22004/) (2025)
- [LaguerreNet: Advancing a Unified Solution for Heterophily and Over-smoothing with Adaptive Continuous Polynomials](https://mlsanity.com/paper/2511.15328/) (2025)
- [Stability of Flow Models for Graph Signals](https://mlsanity.com/paper/2607.07510/) (2026)
- [Learning with Covariance Matrices: Principal Component Analysis Meets Learning with Graphs](https://mlsanity.com/paper/2609.10490/) (2026)
- [Barron Space for Graph Convolution Neural Networks](https://mlsanity.com/paper/2311.02838/) (2023)
- [Online Graph Filtering Over Expanding Graphs](https://mlsanity.com/paper/2409.07204/) (2024)
- [Learning Graph Filters for Structure-Function Coupling based Hub Node Identification](https://mlsanity.com/paper/2410.17410/) (2024)
- [Explainable Spatio-Temporal GCNNs for Irregular Multivariate Time Series: Architecture and Application to ICU Patient Data](https://mlsanity.com/paper/2411.01070/) (2024)
- [Haar-Laplacian for directed graphs](https://mlsanity.com/paper/2411.15527/) (2024)
- [A Fused Gromov-Wasserstein Approach to Subgraph Contrastive Learning](https://mlsanity.com/paper/2502.20885/) (2025)
- [Leveraging Low-rank Factorizations of Conditional Correlation Matrices in Graph Learning](https://mlsanity.com/paper/2506.10628/) (2025)

## Abstract (arXiv)

Filters are fundamental in extracting information from data. For time series and image data that reside on Euclidean domains, filters are the crux of many signal processing and machine learning techniques, including convolutional neural networks. Increasingly, modern data also reside on networks and other irregular domains whose structure is better captured by a graph. To process and learn from such data, graph filters account for the structure of the underlying data domain. In this article, we provide a comprehensive overview of graph filters, including the different filtering categories, design strategies for each type, and trade-offs between different types of graph filters. We discuss how to extend graph filters into filter banks and graph neural networks to enhance the representational power; that is, to model a broader variety of signal classes, data patterns, and relationships. We also showcase the fundamental role of graph filters in signal processing and machine learning applications. Our aim is that this article provides a unifying framework for both beginner and experienced researchers, as well as a common understanding that promotes collaborations at the intersections of signal processing, machine learning, and application domains.