2021/2022
Topological Data Analysis
Code: 104419 ECTS Credits: 6| Degree | Type | Year | Semester |
|---|---|---|---|
| 2503740 Computational Mathematics and Data Analytics | OT | 4 | 1 |
The proposed teaching and assessment methodology that appear in the guide may be subject to changes as a result of the restrictions to face-to-face class attendance imposed by the health authorities.
Contact
- Name:
- Joan Porti Piqué
- Email:
- Joan.Porti@uab.cat
Use of Languages
- Principal working language:
- catalan (cat)
- Some groups entirely in English:
- No
- Some groups entirely in Catalan:
- Yes
- Some groups entirely in Spanish:
- No
Teachers
- Martín-Hernán Campos Heredia
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
Competences
- Apply a critical spirit and rigour for the validation or rejection of your own arguments and those of others.
- Demonstrate a high capacity for abstraction and translation of phenomena and behaviors to mathematical formulations.
- Formulate hypotheses and think up strategies to confirm or refute them.
- Make effective use of bibliographical resources and electronic resources to obtain information.
- Relate new mathematical objects with other known objects and deduce their properties.
- Students must be capable of applying their knowledge to their work or vocation in a professional way and they should have building arguments and problem resolution skills within their area of study.
- Students must be capable of collecting and interpreting relevant data (usually within their area of study) in order to make statements that reflect social, scientific or ethical relevant issues.
- Students must develop the necessary learning skills to undertake further training with a high degree of autonomy.
- Students must have and understand knowledge of an area of study built on the basis of general secondary education, and while it relies on some advanced textbooks it also includes some aspects coming from the forefront of its field of study.
- Using criteria of quality, critically evaluate the work carried out.
- Work cooperatively in a multidisciplinary context assuming and respecting the role of the different members of the team.
Learning Outcomes
- Apply a critical spirit and rigour for the validation or rejection of your own arguments and those of others.
- Contrast, if possible, the use of calculation with the use of abstraction in solving a problem. Evaluate the advantages and disadvantages of both methods.
- Describe the concepts and mathematical objects pertaining to the subject.
- Describe the distinct components of a system and the interactions between them.
- Make effective use of bibliographical resources and electronic resources to obtain information.
- Relate these concepts to methods and objects in other areas.
- Students must be capable of applying their knowledge to their work or vocation in a professional way and they should have building arguments and problem resolution skills within their area of study.
- Students must be capable of collecting and interpreting relevant data (usually within their area of study) in order to make statements that reflect social, scientific or ethical relevant issues.
- Students must develop the necessary learning skills to undertake further training with a high degree of autonomy.
- Students must have and understand knowledge of an area of study built on the basis of general secondary education, and while it relies on some advanced textbooks it also includes some aspects coming from the forefront of its field of study.
- Understand the basic topological invariants relevant to the analysis of data.
- Using criteria of quality, critically evaluate the work carried out.
- Within a problem, distinguish what is important from what is not so as to construct the mathematical model and its resolution.
- Work cooperatively in a multidisciplinary context, taking on and respecting the role of the distinct members in the team.
Content
- Introduction to topology. Graphs and simplicial complexes.
- Homology and Betti numbers.
- Persitent homology and filtrations.
- Applications: entropy, time series, mapper.
Methodology
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.
Activities
| Title | Hours | ECTS | Learning Outcomes |
|---|---|---|---|
| Type: Directed | |||
| Lectures | 26 | 1.04 | 1, 12, 2, 11, 3, 4, 13, 10, 9, 7, 8, 6, 14, 5 |
| Practices with computer | 24 | 0.96 | 1, 12, 2, 11, 3, 4, 13, 10, 9, 7, 8, 6, 14, 5 |
| Type: Supervised | |||
| Tutoring and consultations | 10 | 0.4 | 1, 12, 2, 11, 3, 4, 13, 10, 9, 7, 8, 6, 14, 5 |
| Type: Autonomous | |||
| Independent study and preparation | 45 | 1.8 | 1, 12, 2, 11, 3, 4, 13, 10, 9, 7, 8, 6, 14, 5 |
| Use of sorftware | 30 | 1.2 | 1, 12, 2, 11, 3, 4, 13, 10, 9, 7, 8, 6, 14, 5 |
Assessment
Evaluations is organized as follows:
- First partial test (20%).
- Second partial test (20%).
- Practical sessios (30%).
- Practical final work (20%).
Some of the practical sessions will be evaluated at the end (previously announced). Partial tests and the practical work can be reevaluated, but the contnued evaluation cannot.
Assessment Activities
| Title | Weighting | Hours | ECTS | Learning Outcomes |
|---|---|---|---|---|
| Continued evaluation practices | 30 | 0 | 0 | 1, 12, 2, 11, 3, 4, 13, 10, 9, 7, 8, 6, 14, 5 |
| First partial test theory | 20 | 2.5 | 0.1 | 1, 12, 2, 11, 3, 4, 13, 10, 9, 7, 8, 6, 14, 5 |
| Practices memory | 20 | 10 | 0.4 | 1, 12, 2, 11, 3, 4, 13, 10, 9, 7, 8, 6, 14, 5 |
| Secont partial test theory | 30 | 2.5 | 0.1 | 1, 12, 2, 11, 3, 13, 10, 9, 7, 8, 6, 14, 5 |
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
Software
Compùter practical sessions shall be in Python.