Topological Data Analysis
Code: 104419 ECTS Credits: 6| Degree | Type | Year |
|---|---|---|
| 2503740 Computational Mathematics and Data Analytics | OT | 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.
- CM43 (Competence) Calculate the basic topological invariants relevant to data analysis.
- 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.
- 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 | CM43, KM35, SM42, CM43 |
| Use of sorftware | 30 | 1.2 | CM43, KM35, SM42, CM43 |
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 | |
| First partial test theory | 30 | 2.5 | 0.1 | CM43, KM35, SM42 |
| Presentació final de curs | 30 | 2.5 | 0.1 |
Evaluations is organized as follows:
- Partial test (midterm) (30%)
- Deliveables at practical sessions(40%)
- Final presentation (30%)
- Some of the practical sessions will be evaluated at the end (previously announced). Partial tests and the practical work can be reevaluated, but the continued evaluation cannot.
- The one day assessment (avaluació unica) will take place on the same day as the final course presentations. The one day assessment will consist of the delivery of practicals (different from those carried out during the course), the final presentation and the subsequent completion of the partial test.
- 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
Language list
| Name | Group | Language | Semester | Turn |
|---|---|---|---|---|
| (PAUL) Classroom practices | 1 | Catalan | first semester | morning-mixed |
| (TE) Theory | 1 | Catalan | first semester | morning-mixed |