Algebraic Topology for Data Scientists

TL;DR

This book introduces topological data analysis (TDA) to data scientists, covering foundational algebraic topology concepts, current applications, and advanced topics to enable new insights from data.

Contribution

It provides a comprehensive introduction to algebraic topology and TDA tailored for data scientists, bridging a gap between advanced mathematics and practical data analysis.

Findings

Explains core concepts of algebraic topology relevant to TDA

Details applications of TDA in data science

Discusses advanced topics like cohomology and homotopy in data analysis

Abstract

This book gives a thorough introduction to topological data analysis (TDA), the application of algebraic topology to data science. Algebraic topology is traditionally a very specialized field of math, and most mathematicians have never been exposed to it, let alone data scientists, computer scientists, and analysts. I have three goals in writing this book. The first is to bring people up to speed who are missing a lot of the necessary background. I will describe the topics in point-set topology, abstract algebra, and homology theory needed for a good understanding of TDA. The second is to explain TDA and some current applications and techniques. Finally, I would like to answer some questions about more advanced topics such as cohomology, homotopy, obstruction theory, and Steenrod squares, and what they can tell us about data. It is hoped that readers will acquire the tools to start to think about these topics and where they might fit in.