Week 01 — Motivations and Overview

Why a topologist's tools — persistent homology, Mapper, stability — turn out to be a working data-science primitive.

Lecture

What TDA is and what it isn’t. The shape-of-data thesis. Standard ML features vs topological features. Tour of the rest of the semester.

Read before the lecture

• Carlsson, *Topology and Data* (Bull. AMS 2009)

Code lab

First persistence diagram

Compute persistence diagrams of three point clouds (a noisy circle, a torus, two interlocked circles) using ripser, plot, and interpret.

Notebook: lab01-first-diagrams.ipynb  ·  Dataset: Synthetic, generated in-notebook.

Reference text for this week: chapter 01 of the bilingual notes — EN PDF · FR PDF.