Statistical analysis and parameter selection for Mapper - Archive ouverte HAL
Journal Articles Journal of Machine Learning Research Year : 2018

Statistical analysis and parameter selection for Mapper

Mathieu Carriere
Steve Y. Oudot
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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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Dates and versions

hal-01633106 , version 1 (13-11-2017)
hal-01633106 , version 2 (10-10-2018)

Identifiers

  • HAL Id : hal-01633106 , version 2

Cite

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