(Note: location changed to CCB 102)
Title: Providing Statistical Guarantees for Topological Summaries of Data
Persistent homology is a method for probing topological properties of point clouds and function. The method involves tracking the birth and death of topological features as one varies a tuning parameter. Features with short lifetimes are informally considered to be “topological noise.” I am interested in bringing statistical ideas to persistent homology in order to distinguish topological signal from topological noise and to derive meaningful, yet computable, summaries of large datasets. In this talk, I will define some of the existing topological summaries of data, and show how we can provide statistical guarantees of these summaries.