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Computing Nonlinear Eigenfunctions via Gradient Flow Extinction

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Scale Space and Variational Methods in Computer Vision (SSVM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 11603))

Abstract

In this work we investigate the computation of nonlinear eigenfunctions via the extinction profiles of gradient flows. We analyze a scheme that recursively subtracts such eigenfunctions from given data and show that this procedure yields a decomposition of the data into eigenfunctions in some cases as the 1-dimensional total variation, for instance. We discuss results of numerical experiments in which we use extinction profiles and the gradient flow for the task of spectral graph clustering as used, e.g., in machine learning applications.

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Acknowledgments

This work was supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 777826 (NoMADS). LB and MB acknowledge further support by ERC via Grant EU FP7 – ERC Consolidator Grant 615216 LifeInverse.

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Authors and Affiliations

  1. Department Mathematik, Universität Erlangen-Nürnberg, Cauerstrasse 11, 91058, Erlangen, Germany

    Leon Bungert, Martin Burger & Daniel Tenbrinck

Authors
  1. Leon Bungert
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  2. Martin Burger
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  3. Daniel Tenbrinck
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Corresponding author

Correspondence to Leon Bungert .

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Editors and Affiliations

  1. University of Lübeck, Lübeck, Germany

    Jan Lellmann

  2. University of Erlangen-Nuremberg (FAU), Erlangen, Germany

    Martin Burger

  3. University of Lübeck, Lübeck, Germany

    Jan Modersitzki

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Bungert, L., Burger, M., Tenbrinck, D. (2019). Computing Nonlinear Eigenfunctions via Gradient Flow Extinction. In: Lellmann, J., Burger, M., Modersitzki, J. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2019. Lecture Notes in Computer Science(), vol 11603. Springer, Cham. https://doi.org/10.1007/978-3-030-22368-7_23

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  • DOI: https://doi.org/10.1007/978-3-030-22368-7_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-22367-0

  • Online ISBN: 978-3-030-22368-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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