Algebraic Topology for Data Scientists
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.
Cite
@article{arxiv.2308.10825,
title = {Algebraic Topology for Data Scientists},
author = {Michael S. Postol},
journal= {arXiv preprint arXiv:2308.10825},
year = {2024}
}
Comments
322 pages, 69 figures, 5 tables--New version adds author's note at the beginning of Section 11.10 about some newer work on Steenrod square computation by Lupo, Medina Mardones, and Tauzin. There is a much faster computation method there than the methods I knew about when I wrote the book, and the connection to data science is more clear. Also fixed some more typos