On the Bootstrap for Persistence Diagrams and Landscapes

TL;DR

This paper applies the empirical bootstrap method to persistent homology, enabling the construction of confidence sets for persistence diagrams and bands for persistence landscapes to distinguish signal from noise.

Contribution

It introduces a bootstrap-based statistical framework for quantifying uncertainty in topological data analysis results.

Findings

Confidence sets for persistence diagrams derived

Confidence bands for persistence landscapes established

Method effectively separates topological signal from noise

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 confidence bands for persistence landscapes.