Week 05 — Stability Theorems
Why TDA features can survive noise: the bottleneck-distance stability of diagrams under Hausdorff perturbations.
Week 05 — Stability Theorems
Why TDA features can survive noise: the bottleneck-distance stability of diagrams under Hausdorff perturbations.
Lecture
The bottleneck distance · the stability theorem of Cohen-Steiner-Edelsbrunner-Harer (2007) · interleaving distance and the algebraic stability theorem · what stability buys you in practice.
Read before the lecture
- Cohen-Steiner, Edelsbrunner, Harer, *Stability of Persistence Diagrams* (Discrete Comput. Geom. 2007)
- Chazal, de Silva, Glisse, Oudot, *The Structure and Stability of Persistence Modules*
Problem set
PS3 — Stability arguments
- Prove the bottleneck stability for $\check{C}$ech filtrations from a chosen reference.
- Construct an explicit perturbation showing the stability bound is tight.
Reference text for this week: chapter 05 of the bilingual notes — EN PDF · FR PDF.