Persistence

This is the webpage for the UCR Math Department’s undergraduate research project on persistent homology and topological data analysis. This project is conducted by Joshua Bocanegra, Chris Chebat, Edgar Giovanni Lepe, and Rhiann Zhang, and organized by Jade Master and by Mike Pierce, who can be reached via email at

             

References & Resources

• Persistent Homology: A Non-Mathy Introduction with Examples by Gary Koplik – Exactly as the name suggests, it’s a great introduction with many gifs to build intuition.
• Topological Pattern Recognition for Point Cloud Data by Gunnar Carlsson – The foundational paper on the subject of topological data analysis, with a good exposition.
• A roadmap for the computation of persistent homology by Otter, Porter, Tillmann, Grindrod, and Harrington, with accompanying slides by Nina Otter – The best paper for shopping around for the right piece of software to use.
• A Brief History of Persistence by Jose A. Perea – An eleven page introduction that covers persistence modules and quiver representations.
• Computing Persistent Homology by Zomorodian and Carlsson – If I recall, in this paper they first calculate persistence modules over an arbitrary field. Or over a PID?
• RIVET – a tool for two-parameter persistent homology.
• Persistence Theory: From Quiver Representations to Data Analysis by Steve Oudot
• Barcodes: The Persistent Topology of Data by Robert Ghrist
• Homological Algebra and Data by Robert Ghrist
• Representation Theorem of Persistence Revisited and Generalized Corbet & Kerber
• Categorification of Persistent Homology by Bubenik and Scott
• Tamal Dey’s course on Computational Topology and Data Analysis
• Reference on Persistent Homology Question on MO