mlsanityData to 14 Oct 2026

Graph Filters for Signal Processing and Machine Learning on Graphs

arXiv 2211.08854 ↗First posted 16 Nov 2022eess.SP cs.LGcited by 53

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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.

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

156 of 370 references.

References · 156

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38 more
  1. 2018Graph Convolutional Neural Networks for Web-Scale Recommender Systemscited by 1,138
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50 most cited of 156 All 156 (JSON)

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 7; 2024: 11; 2025: 25; 2026: 10.

53 papers.

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  1. 2023Graph Neural Networks with Learnable and Optimal Polynomial Basescited by 36
  2. 2023Improving Protein Optimization with Smoothed Fitness Landscapescited by 21
  3. 2025Cross-Contrastive Clustering for Multimodal Attributed Graphs with Dual Graph Filteringcited by 14
  4. 2024Spatiotemporal Covariance Neural Networkscited by 9
  5. 2023Fairness-Aware Graph Filter Designcited by 8
  6. 2024Redesigning graph filter-based GNNs to relax the homophily assumptioncited by 8
  7. 2025Graph-Aware Diffusion for Signal Generationcited by 8
  8. 2024Sparse Covariance Neural Networkscited by 7
  9. 2024Fair CoVariance Neural Networkscited by 6
  10. 2023Recovering Missing Node Features with Local Structure-based Embeddingscited by 5
  11. 2025Topological Dictionary Learningcited by 4
  12. 2025Covariance Density Neural Networkscited by 4
38 more
  1. 2025Disentangling Neurodegeneration with Brain Age Gap Prediction Models: A Graph Signal Processing Perspectivecited by 3
  2. 2025KrawtchoukNet: A Unified GNN Solution for Heterophily and Over-smoothing with Adaptive Bounded Polynomialscited by 3
  3. 2023Fairness-aware Optimal Graph Filter Designcited by 2
  4. 2023On the Trade-Off between Stability and Representational Capacity in Graph Neural Networkscited by 2
  5. 2024Online Learning Of Expanding Graphscited by 2
  6. 2025Training-free Adjustable Polynomial Graph Filtering for Ultra-fast Multimodal Recommendationcited by 2
  7. 2025Topological Adaptive Least Mean Squares Algorithms over Simplicial Complexescited by 2
  8. 2025GKNet: Graph Kalman Filtering and Model Inference via Model-based Deep Learningcited by 2
  9. 2025LaguerreNet: Advancing a Unified Solution for Heterophily and Over-smoothing with Adaptive Continuous Polynomialscited by 2
  10. 2026Stability of Flow Models for Graph Signalscited by 2
  11. 2026Learning with Covariance Matrices: Principal Component Analysis Meets Learning with Graphscited by 2
  12. 2023Barron Space for Graph Convolution Neural Networkscited by 1
  13. 2024Online Graph Filtering Over Expanding Graphscited by 1
  14. 2024Learning Graph Filters for Structure-Function Coupling based Hub Node Identificationcited by 1
  15. 2024Explainable Spatio-Temporal GCNNs for Irregular Multivariate Time Series: Architecture and Application to ICU Patient Datacited by 1
  16. 2024Haar-Laplacian for directed graphscited by 1
  17. 2025A Fused Gromov-Wasserstein Approach to Subgraph Contrastive Learningcited by 1
  18. 2025Leveraging Low-rank Factorizations of Conditional Correlation Matrices in Graph Learningcited by 1
  19. 2025Directed Acyclic Graph Convolutional Networkscited by 1
  20. 2025Graph Distribution-valued Signals: A Wasserstein Space Perspectivecited by 1
  21. 2026Which Graph Shift Operator? A Spectral Answer to an Empirical Questioncited by 1
  22. 2024Graph Convolutional Network For Semi-supervised Node Classification With Subgraph Sketchingcited by 0
  23. 2024LASE: Learned Adjacency Spectral Embeddingscited by 0
  24. 2025Converting Transformers into DGNNs Formcited by 0
  25. 2025Cramer-Rao Bounds for Laplacian Matrix Estimationcited by 0
  26. 2025On the Stability of Graph Convolutional Neural Networks: A Probabilistic Perspectivecited by 0
  27. 2025Quantitative Error Feedback for Quantization Noise Reduction of Filtering over Graphscited by 0
  28. 2025SlepNet: Spectral Subgraph Representation Learning for Neural Dynamicscited by 0
  29. 2025Signed Graph Learning: Algorithms and Theorycited by 0
  30. 2025Unrolling Dynamic Programming via Graph Filterscited by 0
  31. 2025A Novel Unified Extended Matrix for Graph Signal Processing: Theory and Applicationcited by 0
  32. 2025CoVariance Filters and Neural Networks over Hilbert Spacescited by 0
  33. 2025Graph Variate Neural Networkscited by 0
  34. 2025Rotation-Parameterized Graph Fractional Fourier Transform: Definition, Properties, and Optimal Filteringcited by 0
  35. 2026Graph Learning Should Move Beyond Restrictive Views of Spectral and Message-Passing GNNscited by 0
  36. 2026Including Node Textual Metadata in Laplacian-constrained Gaussian Graphical Modelscited by 0
  37. 2026Subspace Projection Methods for Fast Spectral Embeddings of Evolving Graphscited by 0
  38. 2026Stochastic Sequential Decision Making over Expanding Networks with Graph Filteringcited by 0

50 most cited of 53 All 53 (JSON)