# Quick List of Resources for Topological Data Analysis with Emphasis on Machine Learning
This is just a quick list of resourses on TDA that I put together for [@rickasaurus](https://twitter.com/rickasaurus) after he was asking for links to papers, books, etc on Twitter and is by no means an exhaustive list.

## Survey Papers
Both Carlsson's and Ghrist's survey papers offer a very good introduction to the subject
* [Topology and Data](http://www.ams.org/journals/bull/2009-46-02/S0273-0979-09-01249-X/S0273-0979-09-01249-X.pdf) by Gunnar Carlsson
* [Barcodes: The Persistent Topology of Data](https://www.math.upenn.edu/~ghrist/preprints/barcodes.pdf) by Robert Ghrist

## Other Papers and Web Resources
* [Extracting insights from the shape of complex data using topology](http://www.nature.com/articles/srep01236) A good introductory paper in Nature on the `Mapper` algorithm.
* [Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition](https://research.math.osu.edu/tgda/mapperPBG.pdf) A more technical presentation of `Mapper`.
* [Topological Data Analysis and Machine Learning Theory](https://www.birs.ca/workshops/2012/12w5081/report12w5081.pdf) Applications of TDA to machine learning.
* Ayasdi, the company founded by Gurjeet Singh and Gunnar Carlsson, has several good [videos and whitepapers](http://www.ayasdi.com/resources) on how they use `Mapper` and TDA in machine learning pipelines.
* [Applied Algebraic Topology Research Network](https://www.ima.umn.edu/topology/) An online research symposium through the IMA that has several recorded talks dealing with TDA and machine learning.

## Software
* [Mapper in Python](http://danifold.net/mapper/)
* [TDA: Statistical Tools for Topological Data Analysis](https://cran.r-project.org/web/packages/TDA/index.html) R package
* [JavaPlex](https://github.com/appliedtopology/javaplex) Persistent Homology in Java and Matlab
* [Perseus](http://www.sas.upenn.edu/~vnanda/perseus/) Persistent Homology in C++

## Books
* [Computational Topology: An Introduction](http://www.amazon.com/Computational-Topology-Introduction-Herbert-Edelsbrunner/dp/0821849255) A good introducgtory book on persistent homology
* [Elementary Applied Topology](https://www.math.upenn.edu/~ghrist/notes.html) A book by Robert Ghrist that goes beyond applications of algebraic toplogy to data analysis, but is a very good read.  There is a very inexpensive print version and the PDF is available for free.
* [Topological Signal Processing](http://www.amazon.com/Topological-Signal-Processing-Mathematical-Engineering/dp/364236103X) Not directly related to data analysis, but a good book on using topological methods in signal processing.