Topological Data Analysis via Undergraduate Linear Algebra

TL;DR

This paper introduces explicit methods for computing persistent homology using undergraduate linear algebra, making topological data analysis more accessible for educational purposes.

Contribution

It provides novel, straightforward linear algebra techniques for calculating persistent (co)homology, simplifying the process for learners and practitioners.

Findings

Explicit linear algebra methods for persistent homology

Educational examples demonstrating the techniques

Simplified computation approach for topological data analysis

Abstract

Topological Data Analysis has grown in popularity in recent years as a way to apply tools from algebraic topology to large data sets. One of the main tools in topological data analysis is persistent homology. This paper uses undergraduate linear algebra to provide explicit methods for, and examples of, computing persistent (co)homology.