On the Bootstrap for Persistence Diagrams and Landscapes

Understand

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.