Computational topology has recently known an important development toward data analysis, giving birth to the eld of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this eld. 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.
['Frédéric Chazal', 'Marc Glisse', 'Catherine Labruère', 'Bertrand Michel']
Optimal rates of convergence for persistence diagrams in Topological Data Analysis