ECE Siminar: Distorted Diffeomorphisms of Small Distortion in Euclidean Space and their Applications to the Parsimonious Representation of Data in Manifold Learning

The parsimonious representation of data is a fundamental problem in many sciences. By this problem, we typically mean, obtaining accurate models of naturally occurring sources of data, obtaining optimal representations of such models and rapidly computing such optimal representations. A basic question which interests us in this talk is when do two sets of point clouds in some containing high dimensional Euclidean space describe the same manifold?" We will address this question now in some sense by talking about our joint work with Charlie Fefferman.