A Practical Introduction to Topological Data Analysis
Persistent Homology is a powerful and flexible tool in the increasingly popular area of Topological Data Analysis. Persistent homology can identify interesting “topological” structures of various dimensions in data. This talk is an introduction to the theory and application of Persistent Homology, and an attempt to explain how Topological Data Analysis is valuable as a complement to Statistical Analysis of data. We will review some highlights from the persistent homology literature across a broad range of areas. We will explain the computation of persistent homology using familiar - as well as unfamiliar - elementary matrix operations, and illustrate and interpret with simple examples computed by hand. We will discuss the mathematical “stability” results that make Persistent Homology insensitive to perturbations or measurements errors in data, and illustrate with live computed examples.