An Introduction to Topological Data Analysis Ball Mapper in Python

Abstract

Visualization of data is an important step in the understanding of data and the evaluation of statistical models. Topological Data Analysis Ball Mapper (TDABM) after Dlotko (2019), provides a model free means to visualize multivariate datasets without information loss. To permit the construction of a TDABM graph, each variable must be ordinal and have sufficiently many values to make a scatterplot of interest. Where a scatterplot works with two, or three, axes, the TDABM graph can handle any number of axes simultaneously. The result is a visualization of the structure of data. The TDABM graph also permits coloration by additional variables, enabling the mapping of outcomes across the joint distribution of axes. The strengths of TDABM for understanding data, and evaluating models, lie behind a rapidly expanding literature. This guide provides an introduction to TDABM with code in Python.

The original BallMapper algorithm is from Dłotko, P. (2019). Ball mapper: A shape summary for topological data analysis. arXiv preprint arXiv:1901.07410