Ulrich Bauer: Ripser - Efficient Computation of Vietoris–Rips Persistence Barcodes
Hausdorff Center for Mathematics via YouTube
Overview
Syllabus
Intro
Vietoris-Rips filtrations
Demo: Ripser
Ripser A software for computing Vietoris-flips persistence barcodes - about 1000 lines of C++ code, no external dependencies
Design goals
The four special ingredients
Matrix reduction algorithm Setting: finite metric space X, points
Compatible basis cycles For a reduced boundary matrix R-D. V, call
Persistent cohomology
Counting cohomology column reductions
Observations
Implicit matrix reduction Standard approach
Oblivious matrix reduction
Natural filtration settings
Fundamental theorem of discrete Morse theory Letf be a discrete Morse function on a cell complex K.
Morse pairs and persistence pairs
Apparent pairs
From Morse theory to persistence and back
Ripser Live: users from 156 different cities
Taught by
Hausdorff Center for Mathematics