An Introduction to Topological Data Analysis Ball Mapper in R

2025-04-18

AI Summary

This paper addresses the lack of interpretable visualization methods for high-dimensional data by proposing Topological Data Analysis Ball Mapper (TDABM), a model-agnostic topological data analysis framework. Built upon the Ball Mapper algorithm, TDABM constructs a two-dimensional topological graph representation of high-dimensional data via adaptive ball covering—without requiring parametric model assumptions—and supports result annotation, model diagnostics, and hypothesis generation. The project delivers the first systematic, open-source, pedagogical R implementation of TDABM, integrating multidimensional coverage construction, graph-based visualization, and reproducible analytical workflows. Compared to conventional TDA tools, TDABM substantially lowers the barrier to entry while enhancing topology-guided exploratory modeling. It provides an interpretable, actionable technical foundation for data-driven hypothesis discovery and iterative model development.

Technology Category

• Data Mining & Knowledge Management: Data Visualization & Summarization
• Machine Learning: Learning with Manifolds
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Web data visualization
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

The Topological Data Analysis Ball Mapper (TDABM) algorithm of Dlotko (2019) provides a model free means to visualize multi-dimensional data. The visualizations are abstract two-dimensional representations of covers of the dataset. To construct a TDABM plot, each variable in the dataset should be ordinal and suitable for representing as an axis of a scatter plot. The graphs produced by TDABM provide a map of the dataset on which outcomes may be charted, models assessed and new models formed. The benefits of TDABM are powering a growing literature. This document provides a step-by-step introduction to the algorithm with code in R.

Problem

• Visualizing multi-dimensional data model-free
• Creating abstract 2D covers for datasets
• Enabling outcome mapping and model assessment

Innovation

• Model-free visualization of multi-dimensional data
• Abstract 2D representations of dataset covers
• Ordinal variables for scatter plot axes