Comparing Metrics on Arbitrary Spaces using Topological Data Analysis

Abstract

We use the notion of topological data analysis to compare metrics on data sets. We provide two different motivating examples for this. The first of these is a point cloud data set that has ${\mathbb{R}}^2$ as its ambient space, and is therefore very visual. the second deals with a very abstract space which arises through the study of non-transitive dice.

17 pages, 2 tables, 6 figures