Week 08 — Distances between Diagrams

How to compare two diagrams, and which comparison is mathematically and statistically defensible.

Lecture

Bottleneck and Wasserstein distances · their stability properties · why $W_p$ for $p < \infty$ is harder to compute · kernels on diagrams (Reininghaus, Sliced-Wasserstein).

Read before the lecture

• Reininghaus et al., *A Stable Multi-Scale Kernel for Topological Machine Learning* (CVPR 2015)

Code lab

Statistical tests on diagrams

Two-sample test on diagrams: simulate two populations differing in $H_1$ noise level, test for a difference using a sliced-Wasserstein kernel and a permutation test.

Notebook: lab04-stat-tests.ipynb  ·  Dataset: Synthetic.

Reference text for this week: chapter 08 of the bilingual notes — EN PDF · FR PDF.