Optimal rates of convergence for persistence diagrams in Topological Data Analysis

Abstract

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.

References in corpus (2)

• Confidence sets for persistence diagrams
• Adaptive Hausdorff estimation of density level sets

Cited by in corpus (6)

• Statistical topological data analysis using persistence landscapes
• Confidence sets for persistence diagrams
• Statistical Analysis and Parameter Selection for Mapper
• Probabilistic Fréchet Means for Time Varying Persistence Diagrams
• Topological reconstruction of compact supports of dependent stationary random variables
• The Interconnectivity Vector: A Finite-Dimensional Vector Representation of Persistent Homology