Topological Data Analysis
Code: 104419 ECTS Credits: 6| Degree | Type | Year |
|---|---|---|
| Computational Mathematics and Data Analytics | OP | 4 |
Contact
- Name:
- Joan Porti Pique
- Email:
- joan.porti@uab.cat
Teachers
- Martin Hernan Campos Heredia
Teaching groups languages
You can view this information at the end of this document.
Prerequisites
Students are required to have followed inear algebra, to have familiarity of the geometric notions of previous years, and to have some knowledge of Python.
Objectives and Contextualisation
The first goal is to introduce the topological features of data (namely, shapes and patterns). We shall learn the methodology do release this information, as well as some applications
Learning Outcomes
- CM43 (Competence) Calculate the basic topological invariants relevant to data analysis.
- KM35 (Knowledge) Define the concepts of topological space and continuity of applications.
- SM42 (Skill) Distinguish, among the different mathematical tools, those that are feasible for implementation from those that are not.
Content
1 Introducció a la topologia
2 Complexos simplicials i homologia
3 Homologia persistent
4 Vectoritzacions
5 Una aplicació: periodicitat de sèries temporals
6 UMAP
Activities and Methodology
| Title | Hours | ECTS | Learning Outcomes |
|---|---|---|---|
| Type: Directed | |||
| Lectures | 25 | 1 | |
| Practices with computer | 24 | 0.96 | |
| Type: Supervised | |||
| Tutoring and consultations | 10 | 0.4 | |
| Type: Autonomous | |||
| Independent study and preparation | 46 | 1.84 | |
| Use of sorftware | 30 | 1.2 |
There is a theoretical part (including exercises sessions) and a practical part with computer.
Annotation: Within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.
Assessment
Continous Assessment Activities
| Title | Weighting | Hours | ECTS | Learning Outcomes |
|---|---|---|---|---|
| Continued evaluation practices | 40 | 10 | 0.4 | CM43, KM35, SM42 |
| First partial test theory | 30 | 2.5 | 0.1 | CM43, KM35, SM42 |
| Presentació final de curs | 30 | 2.5 | 0.1 | CM43, KM35, SM42 |
Evaluations is organized as follows:Assessment is distributed as follows:
Theory first partial exam (30%)
Practice assignments (40%)
Final course presentation (30%)
Practice assignments will be submitted at the end of certain sessions, which will be announced in advance. The theory exam and the final presentation are recoverable, but continuous assessment is not.
A minimum grade of 3.5 is required in each of the three components (exam, assignments, and presentation). If the minimum is not achieved in any of them (after recovering the exam or the presentation), the final grade will be the lower of 4.5 or the grade calculated using the weights above.
The single assessment will take place on the same day as the final course presentations. It will consist of submitting practice assignments (different from those completed during the course), the final presentation, and subsequently taking the theory exam. If necessary, the theory exam and the final presentation can be retaken, but the assignments cannot, just as in the continuous assessment model.
- Disclaimer: I have made my best to translate into English the Catalan version. In the unlikely case of differences between versions, we'll follow the Catalan one.
Bibliography
- Edelsbrunner, Herbert; Harer, John L. Computational topology. An introduction. American Mathematical Society, Providence, RI, 2010. xii+241 pp. ISBN: 978-0-8218-4925-5.
- G. Carlsson, Topology and data, Bull. Amer. Math. Soc. 46 (2009), 255-308.
- R. Kraft, Illustrations of Data Analysis Using the Mapper Algorithm and Persistent Homology, KTH Master's Thesis, 2016
- Gunnar Carlsson, Mikael Vejdemo-Johansoon, Topological data analysis with applications. 2022
- Tamal Krishna Dey, Yusu Wang, Computational topology for data analysis. 2022.
- Jean-Daniel Boissonnat, Frédéric Chazal, Mariette Yvinec, Geometric and Topological Inference, to appear in Cambridge University Press (available at https://inria.hal.science/hal-01615863/)
- https://giotto-ai.github.io/gtda-docs/0.3.0/library.html
Software
Compùter practical sessions shall be in Python. We shall use giotto-tda, built on top of scikit-learn
Groups and Languages
Please note that this information is provisional until 30 November 2025. You can check it through this link. To consult the language you will need to enter the CODE of the subject.
| Name | Group | Language | Semester | Turn |
|---|---|---|---|---|
| (PAUL) Classroom practices | 1 | Catalan | first semester | morning-mixed |
| (TE) Theory | 1 | Catalan | first semester | morning-mixed |