Topological Data Analysis is a promising field in data analysis. Indeed, the hypothesis made on the data are much weaker than the hypothesis behind “usual” machine learning algorithms. Quarantine may be a great time for learning it ;)
This list is not exhaustive, I may have missed important resources. If so, please let me know in the comments!
Articles
Mathematical topic presentations
The following papers are great presentations of the topic:
- Topological Data Analysis by Afra Zomorodian
- Topology and Data by Gunnar Carlsson
- Barcodes: The Persistent Topology of Data by Robert Ghristo
- An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists Frédéric Chazal and Bertrand Michel
TDA applications
- P. Y. Lum et al., “Extracting insights from the shape of complex data using topology,” Scientific Reports, vol. 3, no. 1, Dec. 2013.
- J. Mathews, S. Nadeem, M. Pouryahya, A. Tannenbaum, and J. O. Deasy, “Topological Data Analysis of PAM50 and 21-Gene Breast Cancer Assays:,” bioRxiv, Nov. 2018.
Books
- Computational Topology: An Introduction by Herbert Edelsbrunner and John L. Harer
- Topological Data Analysis for Scientific Visualization (Mathematics and Visualization) by Julien Tierny
- Topology for Computing by Afra J. Zomorodian
Videos
- The Shape of Data
- What can persistent homology see?
A private company, Ayasdi has published many videos on the topic. Most of them are related to real world applications of TDA.
- Machine Intelligence for Banks
- Topological Data Analysis: How Ayasdi used TDA to Solve Complex Problems
And their youtube channel has many others.
Software
Python
- scikit-tda is a recent (first commit in July 2018) addition to scikit
- Mapper
R
- TDA