APPLIED MATH SEMINAR

Speaker: Mauro Maggioni, Duke University

When/where: Tuesday, April 29th, 2:30 p.m., AKW 200

Title: Bi-Lipschitz parametrizations of rough manifolds with eigenfunctions of the Laplacian and heat kernels

Abstract:

"Dimensionality reduction" and "manifold learning" are important tasks in the analysis of large data sets, embedded in high dimensional spaces, that have intrinsic dimensionality much smaller than the dimensionality of the space in which they are embedded. Motivated by these problems, we discuss recent results that show that large pieces of manifolds with metric at least C^\alpha can be parametrized in a bi-Lipschitz fashion by using eigenfunctions of the Laplacian on the manifold, or heat kernels on the manifold. These results are stable under perturbations of the manifold, and sampling, and we expect them to be useful for visualization, exploration and parametrization of data sets, and machine learning in general. This is joint work with P.W. Jones (Yale) and R. Schul (UCLA).