6533b853fe1ef96bd12ac8f5
RESEARCH PRODUCT
Convergence Rates for Persistence Diagram Estimation in Topological Data Analysis
Frédéric ChazalMarc GlisseCatherine LabruèreBertrand Michelsubject
[ MATH ] Mathematics [math][STAT.TH] Statistics [stat]/Statistics Theory [stat.TH][ MATH.MATH-AT ] Mathematics [math]/Algebraic Topology [math.AT][STAT.TH]Statistics [stat]/Statistics Theory [stat.TH][MATH.MATH-AT] Mathematics [math]/Algebraic Topology [math.AT][INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG][ STAT.TH ] Statistics [stat]/Statistics Theory [stat.TH]persistent homologytopological data analysis[INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG][MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT]convergence rates[ INFO.INFO-CG ] Computer Science [cs]/Computational Geometry [cs.CG][MATH]Mathematics [math]ComputingMilieux_MISCELLANEOUSdescription
International audience; Computational topology has recently seen 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 that persistence diagrams can be used as statistics with interesting convergence properties. Some numerical experiments are performed in various contexts to illustrate our results.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2014-06-22 |