On the Bootstrap for Persistence Diagrams and Landscapes

Abstract

Persistent homology probes topological properties from point clouds and functions. By looking at multiple scales simultaneously, one can record the births and deaths of topological features as the scale varies. In this paper we use a statistical technique, the empirical bootstrap, to separate topological signal from topological noise. In particular, we derive confidence sets for persistence diagrams and confi- dence bands for persistence landscapes. The article is published in the author’s wording.