On the bootstrap for persistence diagrams and landscapes

Persistent homology probes topological properties from point clouds and func-tions. 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. 1 ar X i