mlsanityData to 7 Oct 2026

Flow Smoothing and Denoising: Graph Signal Processing in the Edge-Space

arXiv 1808.02111 ↗First posted 6 Aug 2018cs.DM cs.SI cs.SYcited by 37

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Abstract (arXiv)

This paper focuses on devising graph signal processing tools for the treatment of data defined on the edges of a graph. We first show that conventional tools from graph signal processing may not be suitable for the analysis of such signals. More specifically, we discuss how the underlying notion of a `smooth signal' inherited from (the typically considered variants of) the graph Laplacian are not suitable when dealing with edge signals that encode a notion of flow. To overcome this limitation we introduce a class of filters based on the Edge-Laplacian, a special case of the Hodge-Laplacian for simplicial complexes of order one. We demonstrate how this Edge-Laplacian leads to low-pass filters that enforce (approximate) flow-conservation in the processed signals. Moreover, we show how these new filters can be combined with more classical Laplacian-based processing methods on the line-graph. Finally, we illustrate the developed tools by denoising synthetic traffic flows on the London street network.

Key facts. Cited by 37 papers in the map (data through 7 Oct 2026). First posted on arXiv 6 Aug 2018.

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Citing papers per year: 2021: 10; 2022: 6; 2023: 9; 2024: 5; 2025: 3; 2026: 4.

37 papers.

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  1. 2021Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyondcited by 81
  2. 2021Principled Simplicial Neural Networks for Trajectory Predictioncited by 77
  3. 2024Position: Topological Deep Learning is the New Frontier for Relational Learningcited by 65
  4. 2023Deciphering Spatio-Temporal Graph Forecasting: A Causal Lens and Treatmentcited by 47
  5. 2023Architectures of Topological Deep Learning: A Survey of Message-Passing Topological Neural Networkscited by 43
  6. 2021Simplicial Convolutional Neural Networkscited by 40
  7. 2022Spectral Augmentation for Self-Supervised Learning on Graphscited by 38
  8. 2021Signal Processing on Cell Complexescited by 31
  9. 2023Convolutional Learning on Simplicial Complexescited by 26
  10. 2021Beyond Low-Pass Filters: Adaptive Feature Propagation on Graphscited by 18
  11. 2022Simplicial Convolutional Filterscited by 18
  12. 2021Dist2Cycle: A Simplicial Neural Network for Homology Localizationcited by 16
25 more
  1. 2021Finite Impulse Response Filters for Simplicial Complexescited by 15
  2. 2021Signal processing on simplicial complexescited by 12
  3. 2022Restructuring Graph for Higher Homophily via Adaptive Spectral Clusteringcited by 9
  4. 2023Dirac signal processing of higher-order topological signalscited by 9
  5. 2022Convolutional Filtering in Simplicial Complexescited by 8
  6. 2023Cycle Invariant Positional Encoding for Graph Representation Learningcited by 8
  7. 2021Helmholtzian Eigenmap: Topological feature discovery & edge flow learning from point cloud datacited by 7
  8. 2023Representing Edge Flows on Graphs via Sparse Cell Complexescited by 5
  9. 2021Outlier Detection for Trajectories via Flow-embeddingscited by 4
  10. 2022Smoothing with the Best Rectangle Window is Optimal for All Tapered Rectangle Windowscited by 3
  11. 2024Binarized Simplicial Convolutional Neural Networkscited by 3
  12. 2024FTF-ER: Feature-Topology Fusion-Based Experience Replay Method for Continual Graph Learningcited by 3
  13. 2024Imputation of Time-varying Edge Flows in Graphs by Multilinear Kernel Regression and Manifold Learningcited by 3
  14. 2025Matched Topological Subspace Detectorcited by 3
  15. 2026Stationarity and Spectral Characterization of Random Signals on Simplicial Complexescited by 1
  16. 2022An Auto-Regressive Formulation for Smoothing and Moving Mean with Exponentially Tapered Windowscited by 0
  17. 2023Windowed Fourier Analysis for Signal Processing on Graph Bundlescited by 0
  18. 2023Formulation of Weighted Average Smoothing as a Projection of the Origin onto a Convex Polytopecited by 0
  19. 2023Adaptive Spatio-temporal Estimation on the Graph Edges via Line Graph Transformationcited by 0
  20. 2024Introduction to Graph Neural Networks for Machine Learning Engineerscited by 0
  21. 2025Faster Inference of Cell Complexes from Flows via Matrix Factorizationcited by 0
  22. 2025Grassmanian Interpolation of Low-Pass Graph Filters: Theory and Applicationscited by 0
  23. 2026Topological Signal Processing: An Application-Oriented Tutorialcited by 0
  24. 2026Gauge-Invariant, Parameter-Insensitive Regularization for Potential Recovery from Flow on Directed Graphscited by 0
  25. 2026Topological Signal Processing With Unoriented Operatorscited by 0