mlsanityData to 14 Oct 2026

Grassmanian Interpolation of Low-Pass Graph Filters: Theory and Applications

arXiv 2510.23235 ↗First posted 27 Oct 2025cs.LG cs.NA cs.SIcited by 0

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Abstract (arXiv)

Low-pass graph filters are fundamental for signal processing on graphs and other non-Euclidean domains. However, the computation of such filters for parametric graph families can be prohibitively expensive as computation of the corresponding low-frequency subspaces, requires the repeated solution of an eigenvalue problem. We suggest a novel algorithm of low-pass graph filter interpolation based on Riemannian interpolation in normal coordinates on the Grassmann manifold. We derive an error bound estimate for the subspace interpolation and suggest two possible applications for induced parametric graph families. First, we argue that the temporal evolution of the node features may be translated to the evolving graph topology via a similarity correction to adjust the homophily degree of the network. Second, we suggest a dot product graph family induced by a given static graph which allows to infer improved message passing scheme for node classification facilitated by the filter interpolation.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 18 of its 41 references that are in the map. First posted on arXiv 27 Oct 2025.

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18 of 41 references.

References · 18

  1. 2016Geometric deep learning: going beyond Euclidean datacited by 1,048
  2. 2017Graph Signal Processing: Overview, Challenges and Applicationscited by 413
  3. 2019Revisiting Graph Neural Networks: All We Have is Low-Pass Filterscited by 261
  4. 2021Is Homophily a Necessity for Graph Neural Networks?cited by 182
  5. 2017An introduction to Topological Data Analysis: fundamental and practical aspects for data scientistscited by 172
  6. 2018Contextual Stochastic Block Modelscited by 134
  7. 2020Handling Missing Data with Graph Representation Learningcited by 133
  8. 2019Graph Wavelet Neural Networkcited by 131
  9. 2018Connecting the Dots: Identifying Network Structure via Graph Signal Processingcited by 111
  10. 2017Statistical inference on random dot product graphs: a surveycited by 70
  11. 2018Flow Smoothing and Denoising: Graph Signal Processing in the Edge-Spacecited by 37
  12. 2021Signal Processing on Cell Complexescited by 31
6 more
  1. 2023A Survey on Spectral Graph Neural Networkscited by 26
  2. 2020A User Guide to Low-Pass Graph Signal Processing and its Applicationscited by 25
  3. 2020Strong Consistency, Graph Laplacians, and the Stochastic Block Modelcited by 21
  4. 2021Signal processing on simplicial complexescited by 12
  5. 2022Learning time-dependent PDE solver using Message Passing Graph Neural Networkscited by 7
  6. 2022Online Change Point Detection for Weighted and Directed Random Dot Product Graphscited by 6

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