Statistical analysis and parameter selection for Mapper

Abstract : In this article, we study the question of the statistical convergence of the 1-dimensional Mapper to its continuous analogue, the Reeb graph. We show that the Mapper is an optimal estimator of the Reeb graph, which gives, as a byproduct, a method to automatically tune its parameters and compute confidence regions on its topological features, such as its loops and flares. This allows to circumvent the issue of testing a large grid of parameters and keeping the most stable ones in the brute-force setting, which is widely used in visualization, clustering and feature selection with the Mapper.
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Pré-publication, Document de travail
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Contributeur : Mathieu Carriere <>
Soumis le : lundi 13 novembre 2017 - 10:19:21
Dernière modification le : mercredi 12 septembre 2018 - 01:16:14
Document(s) archivé(s) le : mercredi 14 février 2018 - 12:28:52


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  • HAL Id : hal-01633106, version 1


Mathieu Carriere, Bertrand Michel, Steve Y. Oudot. Statistical analysis and parameter selection for Mapper. 2017. 〈hal-01633106〉



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