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Discrete Signal Processing on Graphs: Frequency Analysis

arXiv 1307.0468 ↗First posted 1 Jul 2013cs.SI math.SPcited by 72

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Abstract (arXiv)

Signals and datasets that arise in physical and engineering applications, as well as social, genetics, biomolecular, and many other domains, are becoming increasingly larger and more complex. In contrast to traditional time and image signals, data in these domains are supported by arbitrary graphs. Signal processing on graphs extends concepts and techniques from traditional signal processing to data indexed by generic graphs. This paper studies the concepts of low and high frequencies on graphs, and low-, high-, and band-pass graph filters. In traditional signal processing, there concepts are easily defined because of a natural frequency ordering that has a physical interpretation. For signals residing on graphs, in general, there is no obvious frequency ordering. We propose a definition of total variation for graph signals that naturally leads to a frequency ordering on graphs and defines low-, high-, and band-pass graph signals and filters. We study the design of graph filters with specified frequency response, and illustrate our approach with applications to sensor malfunction detection and data classification.

Key facts. Cited by 72 papers in the map (data through 7 Oct 2026). First posted on arXiv 1 Jul 2013.

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Citing papers per year: 2021: 8; 2022: 18; 2023: 10; 2024: 11; 2025: 16; 2026: 9.

72 papers.

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  1. 2022Benchmarking and Analyzing Point Cloud Classification under Corruptionscited by 70
  2. 2022On the Trade-off between Over-smoothing and Over-squashing in Deep Graph Neural Networkscited by 63
  3. 2022Graph Filters for Signal Processing and Machine Learning on Graphscited by 53
  4. 2021Transferability Properties of Graph Neural Networkscited by 42
  5. 2024Spectrally Pruned Gaussian Fields with Neural Compensationcited by 33
  6. 2023An Attentive Inductive Bias for Sequential Recommendation beyond the Self-Attentioncited by 28
  7. 2023Convolutional Learning on Simplicial Complexescited by 26
  8. 2022A Survey of Graph-based Deep Learning for Anomaly Detection in Distributed Systemscited by 20
  9. 2022Simplicial Convolutional Filterscited by 18
  10. 2022PUFA-GAN: A Frequency-Aware Generative Adversarial Network for 3D Point Cloud Upsamplingcited by 18
  11. 2024FastMAC: Stochastic Spectral Sampling of Correspondence Graphcited by 16
  12. 2021Finite Impulse Response Filters for Simplicial Complexescited by 15
38 more
  1. 2021Untrained Graph Neural Networks for Denoisingcited by 15
  2. 2021Wide and Deep Graph Neural Network with Distributed Online Learningcited by 14
  3. 2023Graph Convolutions Enrich the Self-Attention in Transformers!cited by 11
  4. 2022Signed Graph Neural Networks: A Frequency Perspectivecited by 10
  5. 2023Unsupervised Learning of Sampling Distributions for Particle Filterscited by 8
  6. 2024Two Trades is not Baffled: Condensing Graph via Crafting Rational Gradient Matchingcited by 8
  7. 2024Redesigning graph filter-based GNNs to relax the homophily assumptioncited by 8
  8. 2021Node-Variant Graph Filters in Graph Neural Networkscited by 7
  9. 2021A Computational Framework for Modeling Complex Sensor Network Data Using Graph Signal Processing and Graph Neural Networks in Structural Health Monitoringcited by 6
  10. 2022Spatiotemporal Analysis Using Riemannian Composition of Diffusion Operatorscited by 6
  11. 2022Robust Graph Representation Learning for Local Corruption Recoverycited by 6
  12. 2022Learning Stochastic Graph Neural Networks with Constrained Variancecited by 5
  13. 2023Attentional Graph Neural Network Is All You Need for Robust Massive Network Localizationcited by 5
  14. 2022Community-based anomaly detection using spectral graph filteringcited by 4
  15. 2022Graph Signal Processing for Heterogeneous Change Detection Part I: Vertex Domain Filteringcited by 4
  16. 2022Efficient Signed Graph Sampling via Balancing & Gershgorin Disc Perfect Alignmentcited by 4
  17. 2025Topological Schr"odinger Bridge Matchingcited by 4
  18. 2022What Has Been Enhanced in my Knowledge-Enhanced Language Model?cited by 2
  19. 2023Online Filtering over Expanding Graphscited by 2
  20. 2023Fairness-aware Optimal Graph Filter Designcited by 2
  21. 2025Adapting to Heterophilic Graph Data with Structure-Guided Neighbor Discoverycited by 2
  22. 2025A Graph Signal Processing Framework for Hallucination Detection in Large Language Modelscited by 2
  23. 2026Detecting Contextual Hallucinations in LLMs with Frequency-Aware Attentioncited by 2
  24. 2023Barron Space for Graph Convolution Neural Networkscited by 1
  25. 2023A Poincar'e Inequality and Consistency Results for Signal Sampling on Large Graphscited by 1
  26. 2024Online Graph Filtering Over Expanding Graphscited by 1
  27. 2024Haar-Laplacian for directed graphscited by 1
  28. 2024Structure-Guided Input Graph for GNNs facing Heterophilycited by 1
  29. 2025Deep spatio-temporal point processes: Advances and new directionscited by 1
  30. 2026Stationarity and Spectral Characterization of Random Signals on Simplicial Complexescited by 1
  31. 2026Statistical Testing on Directed Graphs by Surrogate Data Generationcited by 1
  32. 2021Regularized Recovery by Multi-order Partial Hypergraph Total Variationcited by 0
  33. 2021Graphs as Tools to Improve Deep Learning Methodscited by 0
  34. 2022Risk-based regulation for all: The need and a method for a wide adoption solution for data-driven inspection targetingcited by 0
  35. 2022Gaussian Kernel Variance For an Adaptive Learning Method on Signals Over Graphscited by 0
  36. 2022Graph Signal Processing for Heterogeneous Change Detection Part II: Spectral Domain Analysiscited by 0
  37. 2022Forecasting Graph Signals with Recursive MIMO Graph Filterscited by 0
  38. 2023Diffusion Maps for Signal Filtering in Graph Learningcited by 0

50 most cited of 72 All 72 (JSON)