Fall 2016
Colloquia are held on Fridays at 11:30 a.m. in Cullimore Lecture Hall II, unless noted otherwise. Refreshments are served at 11:30 am. For questions about the seminar schedule, please contact Yassine Boubendir.
Date: November 4, 2016
Speaker: Tim Sauer
Department of Mathematics,
George Mason University
Title: "Density Estimation and Topology from Data"
Abstract:
Many system/pattern identification problems can be reduced to the analysis of a point cloud. It is often helpful to consider a "geometric prior", the assumption that data lies near a Riemannian manifold. Statistical methods of density estimation date from the 1980s. Persistent homology was proposed by Carlsson and collaborators in the early 2000s as a means of inferring topological characteristics from the data. I discuss these methods and recent work from our group as an alternative to persistent homology, called consistent homology, which uses density estimation to construct a single unweighted graph that replicates the point cloud homology in the large data limit. We discuss applications of these ideas to image segmentation, pattern analysis, and identification of dynamics.