Week 04 — Barcodes and Persistence Diagrams

Two equivalent visualizations of the same data, each with different statistical and ML affordances.

Lecture

Barcodes vs diagrams · persistence images and landscapes as vectorizations · birth-death normalization · what each visualization optimizes for.

Read before the lecture

• Bubenik, *Statistical topological data analysis using persistence landscapes* (JMLR 2015)

Code lab

Vectorizing persistence diagrams

Take diagrams from week 1’s lab, compute persistence landscapes and images, feed both into a sklearn classifier discriminating the three point-cloud types. Compare with raw-feature baseline.

Notebook: lab02-vectorization.ipynb  ·  Dataset: Same synthetic clouds, plus a 4th class for harder test.

Reference text for this week: chapter 04 of the bilingual notes — EN PDF · FR PDF.