Topological Data Analysis
Code: 104419Credits: 6
| Degree programme | Type | Course |
|---|---|---|
| Computational Mathematics and Data Analytics | OP | 4 |
Contact lecturer
- Name :
- Carlos Broto Blanco
- Email :
- carles.broto@uab.cat
Teaching staff
- Joan Porti Pique
Group languages
You can consult this information at the end of the 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
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 (Calculate the basic topological invariants relevant to data analysis.) Calculate the basic topological invariants relevant to data analysis.
- KM35 (Define the concepts of topological space and continuity of applications.) Define the concepts of topological space and continuity of applications.
- SM42 (Distinguish, among the different mathematical tools, those that are feasible for implementation from those that are not.) Distinguish, among the different mathematical tools, those that are feasible for implementation from those that are not.
Contents
1 Introducció a la topologia
2 Complexos simplicials i homologia
3 Homologia persistent
4 Vectoritzacions
5 Una aplicació: periodicitat de sèries temporals
6 UMAP
Learning activities and methodology
| Title | Hours | ECTS | Learning outcomes |
|---|---|---|---|
| Lectures | 25 | 1 | |
| Tutoring and consultations | 10 | 0.4 | |
| Use of sorftware | 30 | 1.2 | |
| Independent study and preparation | 46 | 1.84 | |
| Classroom and computer practices | 24 | 0.96 |
There is a theoretical part and a practical part that includes exercise sessions and computer practice.
Assessment
Continuous assessment activities
| Title | Weight | Hours | ECTS | Learning outcomes |
|---|---|---|---|---|
| End of course presentation | 30 | 2.5 | 0.1 | CM43, KM35, SM42 |
| Continued evaluation of practices | 40 | 10 | 0.4 | CM43, KM35, SM42 |
| Theory exam | 30 | 2.5 | 0.1 | CM43, KM35, SM42 |
Course grading is structured as follows:
- Practical assignments (40%)
- Theory exam (30%)
- Final presentation (30%)
Practical assignments are completed at the end of designated sessions announced in advance. The theory exam and final presentation can be resat; continuous assessment work cannot.
Each of the three assessment activities (theory exam, practical assignments and presentation) requires a minimum grade of 3.5. If these minimum grades are achieved, the final grade is calculated as the weighted average of the grades obtained in the different activities. Otherwise, the final grade will be limited to 4.5, that is, the lower value between the grade obtained using the standard weighting and 4.5.
Students under the single-assessment system will complete their evaluation on the same day as the final course presentations. This consists of submitting a selected set of practical assignments (chosen from those completed throughout the course), making the final presentation, and then sitting the theory exam. As with continuous assessment, the theory exam and presentation may be resat if needed, but the practical assignments may not.
For this subject, the use of Artificial Intelligence (AI) technologies is allowed exclusively in certain tasks and in the manner that will be duly announced in the subject's Moodle classroom.
Anyone who has not completed assessment activities that add up to a minimum of 50% of the final grade will be considered non-evaluable.
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
Course groups and languages
The information provided is provisional until November 30. After this date, you will be able to consult the language of each group through this link. To access the information, you will need to enter the course CODE
| Type of teaching | Group | Language | Semester | Shift |
|---|---|---|---|---|
| (TE) Theory | 1 | Catalan | first semester | morning-mixed |
| (PAUL) Classroom practices | 1 | Catalan | first semester | morning-mixed |