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Statistical analysis and parameter selection for Mapper

Mathieu Carriere 1 Bertrand Michel 2 Steve Y. Oudot 1
1 DATASHAPE - Understanding the Shape of Data
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
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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https://hal.archives-ouvertes.fr/hal-01633106
Contributor : Steve Oudot <>
Submitted on : Wednesday, October 10, 2018 - 5:37:18 PM
Last modification on : Thursday, June 27, 2019 - 1:36:06 PM

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  • HAL Id : hal-01633106, version 2

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Mathieu Carriere, Bertrand Michel, Steve Y. Oudot. Statistical analysis and parameter selection for Mapper. Journal of Machine Learning Research, Microtome Publishing, 2018. ⟨hal-01633106v2⟩

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