Topological Data Analysis

Course title

Code

SDP-I-13

Study programme

Computer Science (1 year)

Organizer of the study programme (unit, institute, department)

Faculty of Computer Science and Engineering

Degree level (first, second, third cycle)

Second cycle

Academic year / semester

9 / Winter

Number of ECTS credits

Teacher

Prerequisites for enrolling in the course

—

10.

Course objectives (competences)

The study of the material in this course has two goals: the first, to give an introduction to this relatively new area by describing the methods used and their mathematical bases in algebraic topology.
The second goal is to apply TDA methods in processing real data sets, for example: in the process of classification and machine learning, and to investigate whether application will result in improved classification performance versus models that do not include these topological features.

11.

Course content

1. Introduction to basic terms of topology: simplicial complexes, simplicial homology, cubic complexes, persistent homology, Cech complexes, Vietoris-Ripps complexes, CW complexes, filter.
2. Review of digital image processing: persistent barcodes, persistent diagrams, persistent images, persistent image homology.
3. Experiments on the application of TDA methods on synthetically generated and realistic data sets of areas of economics, medicine, genetics, image processing and more. With software tools from Python, R and other programming languages.

12.

Learning methods

Предавања поддржани со презентации преку слајдови, интерактивни предавања, вежби (користење на опрема и софтверски пакети), пример случаи, самостојна изработка и одбрана на проектна задача.

13.

Total available time

6 ECTS x 30 hours = 180 hours

14.

Distribution of the available time

60 + 0 + 45 + 45 + 30 = 180 hours

15.

Forms of teaching activities

15.1.	Lectures – theoretical teaching	60 hours
15.2.	Exercises (laboratory, auditory), seminars, team work	0 hours

16.

Other forms of activities

16.1.	Project assignments	45 hours
16.2.	Individual assignments	45 hours
16.3.	Home study	30 hours

17.

Grading

17.1.	Tests	0 points
17.2.	Seminar paper / project (presentation: written and oral)	45 points
17.3.	Activity and participation	10 points
17.4.	Final exam	30 points

18.

Grading criteria (points / grade)

up to 50 points	5 (five) (F)
from 51 to 60 points	6 (six) (E)
from 61 to 70 points	7 (seven) (D)
from 71 to 80 points	8 (eight) (C)
from 81 to 90 points	9 (nine) (B)
from 91 to 100 points	10 (ten) (A)

19.

Requirements for signature and taking the final exam

NULL

20.

Language of instruction

Macedonian

21.

Method of monitoring teaching quality

internal evaluation and surveys

22.

Literature

22.1.	Required literature 1. Edelsbrunner, H.; Harer, JL. \| Computational Topology: An Introduction \| Amer Math Soc. Providence, RI \| 2010 2. Adams, J.F. \| Stable homotopy and generalized homology \| University of Chicago Press \| 2013
22.2.	Additional literature No. Author Title Publisher Year