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.

Minor modifications

References in corpus (2)

• Topological Methods for Exploring Low-density States in Biomolecular Folding Pathways
• Optimal rates of convergence for persistence diagrams in Topological Data Analysis

Cited by in corpus (7)

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• Probabilistic Convergence and Stability of Random Mapper Graphs
• An Introduction to Topological Data Analysis for Physicists: From LGM to FRBs
• Genomics Data Analysis via Spectral Shape and Topology
• Interesting Paths in the Mapper
• Visualizing Image Content to Explain Novel Image Discovery
• Multimapper: Data Density Sensitive Topological Visualization