Open Collections

Description

Many topological computation tasks, as well as stability results, assume that the input is a "clean" (finite) metric space or with very limited type of noise (e.g, with bounded Hausdorff-type distance). In this talk, I will describe three different ways to model noise in metric, and how to perform denoising so as to produce the more friendly form of Hausdorff-type noise. I will specifically focus on the case when the target metric is induced from a graph; however the observed graph is a (randomly) perturbed version of the true graph. I will also discuss some open problems at the end.