This is just a quick list of resourses on TDA that I put together for @rickasaurus after he was asking for links to papers, books, etc on Twitter and is by no means an exhaustive list.
Both Carlsson's and Ghrist's survey papers offer a very good introduction to the subject
- Topology and Data by Gunnar Carlsson
- Barcodes: The Persistent Topology of Data by Robert Ghrist
- Extracting insights from the shape of complex data using topology A good introductory paper in Nature on the
Mapperalgorithm. - Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition A more technical presentation of
Mapper. - Topological Data Analysis and Machine Learning Theory Applications of TDA to machine learning.
- Ayasdi, the company founded by Gurjeet Singh and Gunnar Carlsson, has several good videos and whitepapers on how they use
Mapperand TDA in machine learning pipelines. - Applied Algebraic Topology Research Network An online research symposium through the IMA that has several recorded talks dealing with TDA and machine learning.
- Mapper in Python
- TDA: Statistical Tools for Topological Data Analysis R package
- JavaPlex Persistent Homology in Java and Matlab
- Perseus Persistent Homology in C++
- Computational Topology: An Introduction A good introducgtory book on persistent homology
- Elementary Applied Topology 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 Not directly related to data analysis, but a good book on using topological methods in signal processing.