  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.
