ballmapper: Applying Topological Data Analysis Ball Mapper in Stata

TL;DR

This paper introduces the Ball Mapper Topological Data Analysis tool for Stata, enabling model-free visualization of complex multivariate data without dimensionality reduction, preserving data structure and allowing variable coloring.

Contribution

It provides an introduction to TDABM and implements the Ball Mapper algorithm in a Stata package, expanding its accessibility for data analysis.

Findings

Enables visualization of high-dimensional data without information loss

Supports coloring by additional variables or residuals

Applicable across diverse fields like finance and medicine

Abstract

Topological Data Analysis Ball Mapper (TDABM) offers a model-free visualization of multivariate data which does not necessitate the information loss associated with dimensionality reduction. TDABM Dlotko (2019) produces a cover of a multidimensional point cloud using equal size balls, the radius of the ball is the only parameter. A TDABM visualization retains the full structure of the data. The graphs produced by TDABM can convey coloration according to further variables, model residuals, or variables within the multivariate data. An expanding literature makes use of the power of TDABM across Finance, Economics, Geography, Medicine and Chemistry amongst others. We provide an introduction to TDABM and the \texttt{ballmapper} package for Stata.