mlsanityData to 7 Oct 2026

Windowed Fourier Analysis for Signal Processing on Graph Bundles

arXiv 2302.05592 ↗First posted 11 Feb 2023eess.SP stat.MLcited by 0

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Abstract (arXiv)

We consider the task of representing signals supported on graph bundles, which are generalizations of product graphs that allow for "twists" in the product structure. Leveraging the localized product structure of a graph bundle, we demonstrate how a suitable partition of unity over the base graph can be used to lift the signal on the graph into a space where a product factorization can be readily applied. Motivated by the locality of this procedure, we demonstrate that bases for the signal spaces of the components of the graph bundle can be lifted in the same way, yielding a basis for the signal space of the total graph. We demonstrate this construction on synthetic graphs, as well as with an analysis of the energy landscape of conformational manifolds in stereochemistry.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 15 of its 34 references that are in the map. First posted on arXiv 11 Feb 2023.

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15 of 34 references.

References · 15

  1. 2019Topological Signal Processing over Simplicial Complexescited by 94
  2. 2021Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyondcited by 81
  3. 2018Flow Smoothing and Denoising: Graph Signal Processing in the Edge-Spacecited by 37
  4. 2019Graph-based Semi-Supervised & Active Learning for Edge Flowscited by 25
  5. 2013Vertex-Frequency Analysis on Graphscited by 24
  6. 2013Spectrum-Adapted Tight Graph Wavelet and Vertex-Frequency Framescited by 15
  7. 2021Finite Impulse Response Filters for Simplicial Complexescited by 15
  8. 2020Multi-way Graph Signal Processing on Tensors: Integrative analysis of irregular geometriescited by 12
  9. 2022Enhanced graph-learning schemes driven by similar distributions of motifscited by 11
  10. 2021Approximate and discrete Euclidean vector bundlescited by 7
  11. 2022FibeRed: Fiberwise Dimensionality Reduction of Topologically Complex Data with Vector Bundlescited by 7
  12. 2022On Local Distributions in Graph Signal Processingcited by 6
3 more
  1. 2020Partition of Unity Methods for Signal Processing on Graphscited by 5
  2. 2018Sampling and Reconstruction of Signals on Product Graphscited by 4
  3. 2018Sampling Theory for Graph Signals on Product Graphscited by 1

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