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Journal Articles Journal of Machine Learning Research Year : 2015

Convergence Rates for Persistence Diagram Estimation in Topological Data Analysis

Frédéric Chazal
Marc Glisse

Abstract

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.
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hal-01284275 , version 1 (07-03-2016)

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Frédéric Chazal, Marc Glisse, Catherine Labruère, Bertrand Michel. Convergence Rates for Persistence Diagram Estimation in Topological Data Analysis. Journal of Machine Learning Research, 2015, 16, pp.3603-3635. ⟨10.5555/2789272.2912112⟩. ⟨hal-01284275⟩
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