Ulrich Bauer: Ripser - Efficient Computation of Vietoris–Rips Persistence Barcodes

Ulrich Bauer: Ripser - Efficient Computation of Vietoris–Rips Persistence Barcodes

Hausdorff Center for Mathematics via YouTube Direct link

The four special ingredients

6 of 19

6 of 19

The four special ingredients

Class Central Classrooms beta

YouTube videos curated by Class Central.

Classroom Contents

Ulrich Bauer: Ripser - Efficient Computation of Vietoris–Rips Persistence Barcodes

Automatically move to the next video in the Classroom when playback concludes

  1. 1 Intro
  2. 2 Vietoris-Rips filtrations
  3. 3 Demo: Ripser
  4. 4 Ripser A software for computing Vietoris-flips persistence barcodes - about 1000 lines of C++ code, no external dependencies
  5. 5 Design goals
  6. 6 The four special ingredients
  7. 7 Matrix reduction algorithm Setting: finite metric space X, points
  8. 8 Compatible basis cycles For a reduced boundary matrix R-D. V, call
  9. 9 Persistent cohomology
  10. 10 Counting cohomology column reductions
  11. 11 Observations
  12. 12 Implicit matrix reduction Standard approach
  13. 13 Oblivious matrix reduction
  14. 14 Natural filtration settings
  15. 15 Fundamental theorem of discrete Morse theory Letf be a discrete Morse function on a cell complex K.
  16. 16 Morse pairs and persistence pairs
  17. 17 Apparent pairs
  18. 18 From Morse theory to persistence and back
  19. 19 Ripser Live: users from 156 different cities

Never Stop Learning.

Get personalized course recommendations, track subjects and courses with reminders, and more.

Someone learning on their laptop while sitting on the floor.