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Node-Binded Communities for Interpolation on Graphs

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Numerical Computations: Theory and Algorithms (NUMTA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14477))

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Abstract

Partition of unity methods (PUMs) on graphs represent straightforward and remarkably adaptable auxiliary techniques for graph signal processing. By relying solely on the intrinsic graph structure, we propose the generation of a partition of unity through centrality measures and modularity. Subsequently, we integrate PUMs with a local graph basis function (GBF) approximation approach to achieve low-cost global interpolation schemes.

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References

  1. Cavoretto, R., De Rossi, A.: Error indicators and refinement strategies for solving Poisson problems through a RBF partition of unity collocation scheme. Appl. Math. Comput. 369, 124824 (2020)

    MathSciNet  MATH  Google Scholar 

  2. Cavoretto, R., De Rossi, A., Erb, W.: GBFPUM - A MATLAB package for partition of unity based signal interpolation and approximation on graphs. Dolomites Res. Notes Approx. 15, 25–34 (2022)

    MathSciNet  MATH  Google Scholar 

  3. Cavoretto, R., De Rossi, A., Erb, W.: Partition of Unity Methods for Signal Processing on Graphs. J. Fourier Anal. Appl. 27, Art. 66 (2021)

    Google Scholar 

  4. Erb, W.: Graph signal interpolation with positive definite graph basis functions. Appl. Comput. Harmon. Anal. 60, 368–395 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  5. Erb, W.: Semi-Supervised Learning on Graphs with Feature-Augmented Graph Basis Functions. arXiv:2003.07646 (2020)

  6. Fasshauer, G.E., McCourt, M.J.: Kernel-based Approximation Methods Using MATLAB, p. 536. World Scientific, Singapore (2015)

    Book  MATH  Google Scholar 

  7. Newman, M.: Networks: An Introduction. OUP Oxford, p. 784 (2010)

    Google Scholar 

  8. Ortega, A., Frossard, P., Kovačević, J., Moura, J.M.F., Vandergheynst, P.: Graph signal processing: overview, challenges, and applications. Proc. IEEE 106(5), 808–828 (2018)

    Article  MATH  Google Scholar 

  9. Pesenson, I.Z.: Variational splines and Paley-Wiener spaces on combinatorial graphs. Constr. Approx. 29(1), 1–21 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  10. Rossi, R.A., Ahmed, N.K.: The Network Data Repository with Interactive Graph Analytics and Visualization. In: Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence (2015). http://networkrepository.com

    Google Scholar 

  11. Schaback, R., Wendland, H.: Approximation by positive definite kernels. In: Advanced Problems in Constructive Approximation, Birkhäuser Verlag, Basel, pp. 203–222 (2003)

    Google Scholar 

  12. Shin, H., Park, J., Kang, D.: A graph-cut-based approach to community detection in networks. Appl. Sci. 12, 6218 (2022)

    Article  MATH  Google Scholar 

  13. Stanković, L., Daković, L., Sejdić, E.: Introduction to graph signal processing, pp. 3–108. Springer, In Vertex-Frequency Analysis of Graph Signals (2019)

    Google Scholar 

  14. Ward, J.P., Narcowich, F.J., Ward, J.L.: Interpolating splines on graphs for data science applications. Appl. Comput. Harm. Anal. 49(2), 540–557 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  15. Wendland, H.: Scattered Data Approximation, p. 336. Cambridge University Press, Cambridge (2005)

    MATH  Google Scholar 

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Acknowledgments

The authors sincerely thank the reviewers for the careful reading and valuable comments on the paper. This research has been accomplished within the RITA “Research ITalian network on Approximation” and the UMI Group TAA“Approximation Theory and Applications”. This work has been supported by the INdAM–GNCS 2022 Project “Computational methods for kernel-based approximation and its applications”, code CUP\(\_\)E55F22000270001, and by the Spoke “FutureHPC & BigData” of the ICSC - National Research Center in"High-Performance Computing, Big Data and Quantum Computing", funded by European Union - NextGenerationEU. Moreover, the work has been supported by the Fondazione CRT, project 2022 “Modelli matematici e algoritmi predittivi di intelligenza artificiale per la mobilit\(\grave{\text {a}}\) sostenibile”.

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Authors and Affiliations

  1. Department of Mathematics “Giuseppe Peano”, University of Torino, via Carlo Alberto 10, 10123, Torino, Italy

    Alessandra De Rossi, Sandro Lancellotti & Federico Romaniello

Authors
  1. Alessandra De Rossi
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  2. Sandro Lancellotti
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  3. Federico Romaniello
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Correspondence to Alessandra De Rossi .

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Editors and Affiliations

  1. University of Calabria, Rende, Italy

    Yaroslav D. Sergeyev

  2. University of Calabria, Rende, Italy

    Dmitri E. Kvasov

  3. University of Calabria, Rende, Italy

    Annabella Astorino

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De Rossi, A., Lancellotti, S., Romaniello, F. (2025). Node-Binded Communities for Interpolation on Graphs. In: Sergeyev, Y.D., Kvasov, D.E., Astorino, A. (eds) Numerical Computations: Theory and Algorithms. NUMTA 2023. Lecture Notes in Computer Science, vol 14477. Springer, Cham. https://doi.org/10.1007/978-3-031-81244-6_20

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  • DOI: https://doi.org/10.1007/978-3-031-81244-6_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-81243-9

  • Online ISBN: 978-3-031-81244-6

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