Computing Nonlinear Eigenfunctions via Gradient Flow Extinction

  • Leon BungertEmail author
  • Martin Burger
  • Daniel Tenbrinck
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11603)


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.


Nonlinear eigenfunctions Spectral decompositions Gradient flows Extinction profiles Graph clustering 



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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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department MathematikUniversität Erlangen-NürnbergErlangenGermany

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