An Introduction to Topological Data Analysis: Fundamental and Practical Aspects for Data Scientists

By Frédéric Chazal et al

Published on Feb. 26, 2021

Read the original document by opening this link in a new tab.

Table of Contents

1. Introduction and motivation
2. Metric spaces, covers and simplicial complexes
3. Using covers and nerves for exploratory data analysis and visualization: the Mapper algorithm

Summary

Topological Data Analysis (TDA) is a recent and fast-growing field that provides new topological and geometric tools for inferring relevant features from complex data. This paper serves as a brief introduction to basic fundamental and practical aspects of TDA for non-experts. It covers the motivation behind TDA, the pipeline involved in TDA, statistical approaches to TDA, applications of TDA in data science, and the use of covers and nerves for exploratory data analysis and visualization through the Mapper algorithm.