Stitch Fix for Mapper and Topological Gains

TL;DR

This paper explores a method to combine univariate mappers into a bivariate mapper and analyzes topological information gains during this process, with visualizations of these gains in mapper graphs.

Contribution

It introduces a novel approach for stitching univariate mappers into a bivariate mapper and studies associated topological information gains.

Findings

Method for stitching univariate mappers into a bivariate mapper

Topological gains can be quantified during the stitching process

Visualizations of topological gains in mapper graphs

Abstract

The mapper construction is a powerful tool from topological data analysis that is designed for the analysis and visualization of multivariate data. In this paper, we investigate a method for stitching a pair of univariate mappers together into a bivariate mapper, and study topological notions of information gains, referred to as topological gains, during such a process. We further provide implementations that visualize such topological gains for mapper graphs.