26,748 research outputs found
On the Bootstrap for Persistence Diagrams and Landscapes
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
Optimal rates of convergence for persistence diagrams in Topological Data Analysis
Computational topology has recently known an important development toward
data analysis, giving birth to the field of topological data analysis.
Topological persistence, or persistent homology, appears as a fundamental tool
in this field. In this paper, we study topological persistence in general
metric spaces, with a statistical approach. We show that the use of persistent
homology can be naturally considered in general statistical frameworks and
persistence diagrams can be used as statistics with interesting convergence
properties. Some numerical experiments are performed in various contexts to
illustrate our results
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