Statistical topological data analysis: Rescaling the persistence diagram

Speaker(s): 
Wolfgang Polonik (UC Davis)
Date: 
Wednesday, July 12, 2017 - 10:00am
Location: 
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

A persistence diagram (PD) is one of the basic objects underlying topological data analysis. It is used to analyze topological and geometric features of an underlying space _M_, assuming availability of a random sample from _M_. Existing approaches for such analyses will be reviewed briefly, and their benefits and shortcomings will be discussed. Then we introduce ideas for rescaling PDs, which enables the derivation of novel limit theorems for the total k persistence, and other functionals of PDs. The long-term goal of studying the rescaling of PDs is to develop novel types of statistical analysis of persistence diagrams.