Confidence sets for persistence diagrams

TL;DR

This paper introduces statistical confidence sets for persistent homology, enabling the differentiation of true topological features from noise in point cloud data.

Contribution

It develops a novel statistical framework for persistent homology, providing confidence sets to distinguish signal from noise.

Findings

Confidence sets effectively identify significant topological features.

Method improves robustness of persistent homology analysis.

Applicable to various data types and dimensions.

Abstract

Persistent homology is a method for probing topological properties of point clouds and functions. The method involves tracking the birth and death of topological features (2000) as one varies a tuning parameter. Features with short lifetimes are informally considered to be "topological noise," and those with a long lifetime are considered to be "topological signal." In this paper, we bring some statistical ideas to persistent homology. In particular, we derive confidence sets that allow us to separate topological signal from topological noise.