Codes and Expansions (CodEx) Seminar

Bernhard Bodmann (University of Houston):
Spotting irregularities with reaction and diffusion: A scattering transform on graphs and extremes in log-normal random walks

This talk discusses a version of Mallat's scattering transform for random signals on graphs, which is based on the diffusion semigroup associated with graph Laplacians. The decay of the norm in the layers of the scattering transform is controlled by regularity properties of the signal. For log-normal random walks indexed by graphs, this helps evaluate the consistency between observations and the selection of model parameters, as a type of goodness-of-fit test. The theoretical results are illustrated with finding extremes in traffic counts which exhibit characteristic daily and weekly periodicities.