Analyse statistique de l'algorithme Mapper

The Mapper algorithm is a method for topological data analysis  by Gurjeet Singh, Facundo Mémoli and Gunnar Carlsson. In this work, 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 iswidely used in visualization, clustering and feature selection with the Mapper.

Travail en collaboration avec Mathieu Carriere (INRIA DataShape) and Steve Oudot (INRIA DataShape)