# Computing Nonlinear Eigenfunctions via Gradient Flow Extinction

## TL;DR

This paper explores a method for computing nonlinear eigenfunctions using gradient flow extinction profiles, enabling data decomposition and applications like spectral graph clustering in machine learning.

## Contribution

It introduces a recursive scheme for extracting nonlinear eigenfunctions from data via gradient flow extinction profiles, with analysis and numerical experiments.

## Key findings

- The scheme can decompose data into eigenfunctions such as total variation.
- Numerical experiments demonstrate effectiveness in spectral graph clustering.
- The method provides a new approach for nonlinear eigenfunction computation.

## 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.