Introduction to Topological Data Analysis
A workshop-style course introducing the foundations of TDA — persistent homology, filtrations, and applications to data science. Designed for graduate students and researchers at AIMS and partner institutions.
Instructor: Dr. Yae Ulrich Gaba
Term: Workshop
Location: AIMS Rwanda / Quantum Leap Africa, Kigali
Time: Self-paced / Workshop sessions
Course Overview
This workshop-style course introduces the mathematical foundations of Topological Data Analysis (TDA) and demonstrates how topological methods can extract meaningful structure from complex datasets.
Participants will learn:
- The mathematical language of topology relevant to data analysis
- How to compute persistent homology from point clouds and graphs
- Practical Python tools for TDA (Ripser, GUDHI, scikit-tda)
- How to integrate TDA features into machine learning pipelines
Prerequisites
- Linear algebra fundamentals
- Basic Python programming
- Familiarity with data science concepts (helpful but not required)
References
- The Shape of Data by Farrelly & Gaba (No Starch Press)
- Computational Topology by Edelsbrunner & Harer
- Topological Data Analysis with Applications by Carlsson & Vejdemo-Johansson
Schedule
| Week | Date | Topic | Materials |
|---|---|---|---|
| 1 | Session 1 | What is Topology? From Abstract Spaces to Data Topological spaces, continuous maps, homeomorphisms. Motivation: why shape matters in data. | |
| 2 | Session 2 | Simplicial Complexes and Filtrations Simplices, Vietoris-Rips complexes, Cech complexes. Building filtrations from point clouds. | |
| 3 | Session 3 | Persistent Homology Homology groups, Betti numbers, persistence diagrams and barcodes. The stability theorem. | |
| 4 | Session 4 | TDA in Practice: Python Tools Hands-on: Ripser, GUDHI, scikit-tda. Computing persistence from real datasets. | |
| 5 | Session 5 | Applications: TDA Meets Machine Learning Persistence landscapes, vectorization, TDA features in ML pipelines. Case studies. |