TDA

Suggested Readings, Videos, etc.

Readings:
Topology and Data by Gunnar Carlsson
Barcodes: The Persistent Topology of Data by Robert Ghrist
Simplicial Models and Topological Inference in Biological Systems by Vidit Nanda and Radmila Sazdanovic

Videos:
Matthew Wright’s Introduction to Persistent Homology
Gunnar Carlsson’s Introduction to Topological Data Analysis
Michael Lesnick’s Topological Data Analysis and Persistent Homology
Vidit Nanda’s Topological Data Analysis

TDA applied to neuroscience

Chad Giusti’s list of TDA and neuroscience paper’s bibliography: http://www.chadgiusti.com/bib.html

 

For directed simplicial complexes and its usage in neuroscience:
https://arxiv.org/abs/1601.01580
and the Phat based software package here:
http://neurotop.gforge.inria.fr/

For an application of topological invariant to understand shape of neurons have a look here:

https://arxiv.org/abs/1603.08432

 

Papers and links about TDA software

A roadmap for the computation of persistent homology, Nina Otter, Mason A. Porter, Ulrike Tillmann, Peter Grindrod, Heather A. Harrington https://arxiv.org/abs/1506.08903

Peter Bubenik’s Intro to TDA page (includes worksheet and files for R workshop including Perseus and Persistence Landscape Toolbox http://people.clas.ufl.edu/peterbubenik/intro-to-tda/

Papers containing theory behind the software packages:
B) For Phat and Dipha: https://arxiv.org/abs/1303.0477

Software Guides:
For Gudhi, JavaPlex, and PHAT (scroll down to the “Computational Topology” section)

Software

Data and instructions to play with Gudhi are available here: