Computing Nonlinear Eigenfunctions via Gradient Flow Extinction
This work addresses a computational challenge in machine learning for tasks like spectral graph clustering, but it appears incremental as it builds on existing gradient flow and extinction profile methods.
The paper tackles the problem of computing nonlinear eigenfunctions by using extinction profiles of gradient flows, and demonstrates that recursively subtracting these eigenfunctions can decompose data, as shown with 1-dimensional total variation, and applies the method to spectral graph clustering in numerical experiments.
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.