Week 07 — The Mapper Algorithm

TDA's exploratory-analysis cousin: build a topological skeleton of a dataset, label it, look at it.

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Week 07 — The Mapper Algorithm

TDA's exploratory-analysis cousin: build a topological skeleton of a dataset, label it, look at it.

Lecture

Filter functions · covers and pullbacks · clustering on pullback subsets · the Mapper graph as visual summary · choices that matter (filter, cover, clusterer) and how to choose them.

Read before the lecture

  • Singh, Mémoli, Carlsson, *Topological Methods for the Analysis of High-Dimensional Data Sets* (SPBG 2007)

Problem set

PS4 — Mapper sensitivity

  1. Build a Mapper graph on the iris dataset with three filter functions; characterize how the graph changes.
  2. Construct a dataset where Mapper succeeds and standard $k$-means fails, and vice versa.

Reference text for this week: chapter 07 of the bilingual notes — EN PDF · FR PDF.