This article is cited in 12 papers

On the Bootstrap for Persistence Diagrams and Landscapes

F. Chazal^a, B. T. Fasy^b, F. Lecci^c, A. Rinaldo^c, A. Singh^d, L. Wasserman<sup>c

a</sup> INRIA Saclay
^b Computer Science Department, Tulane University, Stanley Thomas 303 New Orleans, LA 70118
^c Department of Statistics, Carnegie Mellon University, Baker Hall 132 Pittsburgh, PA 15213
^d Machine Learning Department, Carnegie Mellon University, Gates Hillman Centers, 8203 5000 Forbes Avenue Pittsburgh, PA 15213-3891

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.
The article is published in the author's wording.

Keywords: persistent homology, bootstrap, topological data analysis.

UDC: 512.664

Received: 01.11.2013

Language: English