catanzaromj/MBDS19_TDA

A repo for a tutorial on Topological Data Analysis for the Midwest Big Data Summer School in 2019 in Ames, Iowa.

An introduction to Topological Data Analysis

A repository for a tutorial on Topological Data Analysis (TDA) for the Midwest Big Data Summer School in 2019 in Ames, Iowa.

This tutorial covers persistent homology and mapper, two of the main tools used in TDA.

Persistent Homology

For persistent homology, we use the Ripser algorithm, a very efficient C++ implementation of persistence. To simplify the presentation and make it easier to get started, we rely on live.ripser.org for the actual calculation.

Mapper

We use kepler-mapper for our mapper implementation. Kepler-mapper is written in python, and easily combines with other machine learning packages, like scikit-learn for example.

Other tutorials

There are a variety of excellent and much more thorough tutorials available online by experts in the field. Some of the data sets in this tutorial are either motivated by or come directly from the following:

• Charleston-TDA-ML. A tutorial on Persistent Homology written by Henry Adams, Melissa McGuirl, and Yitzchak Solomon.

• Peter Bubenik's TDA with R worksheet. A tutorial on using R to analyze data with Persistence Landscapes.

• MAA-NCS18. Matt Zabka's Persistence Homology tutorial.

• R-TDA tutorial. An R-TDA worksheet tutorial written by Jisu Kim.

This list is nowhere near complete, and there are lots of other great tutorials for learning TDA.