Topological Data Analysis

On this page I have a number of items to get the interested reader started with persistent homology and topological data analysis (TDA). If you know linear algebra you are ready to start! If you you’ve never heard of linear algebra, you can still learn what TDA is about with this article on TDA and Pokemon

Introduction to Topological Data Analysis and Persistent Homology

Simplicial Homology

The main technical tool for persistent homology is simplicial homology. For persistent homology, we use coefficients in a field. So simplicial k-chains are vectors and the set of simplicial k-chains is a vector space. Furthermore, the boundary map is a linear transformation. For finite simplices, it is represented by a matrix.

Topological Data Analysis with R

If you want to get started doing topological data analysis.

Topological Data Analysis and Persistent Homology

Here are some recent introductory articles. If you want to learn more about the subject I would recommend starting here. The first three are mathematical, the fourth emphasizes connections to data science, and the fifth is more statistical.

There is a Wikipedia page.

The following slightly older introductory articles provide background, some mathematical details and a few applications.

The following are more technical summaries of some of the main results in the field.

For a serious introduction, I highly recommend the following new book. It is an excellent resource for mathematics graduate students wanting to learn the subject.

Topological Data Analysis and Deep Learning