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.
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https://hal.archives-ouvertes.fr/hal-00827162
Contributeur : Frédéric Chazal <>
Soumis le : mardi 28 mai 2013 - 21:47:23
Dernière modification le : samedi 24 novembre 2018 - 01:29:40

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  • HAL Id : hal-00827162, version 1
  • ARXIV : 1305.6239

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Frédéric Chazal, Marc Glisse, Catherine Labruère, Bertrand Michel. Optimal rates of convergence for persistence diagrams in Topological Data Analysis. 2013. 〈hal-00827162〉

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