Statistical Analysis and Parameter Selection for Mapper
By Mathieu Carrière, Bertrand Michel, Steve Y. Oudot. 2017
113 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Mathematical Physics, Molecular Biology
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Citations in the corpus
- An Introduction to Topological Data Analysis: Fundamental and Practical Aspects for Data Scientists (2017, methodology): “Based on the results on stability and the structure of Mapper proposed in Carrière and Oudot (2015), advances towards a statistically wellfounded version of Mapper have been obtained recently in Carrière et al.”