Topological Data Analysis

1.

Subject title

Topological Data Analysis

Тополошка анализа на податоци

2.

Code

SDP-I-13

3.

Study program

Cloud Computing, Data science in computer science and engineering, Bioinformatics, Security, Cryptography and Coding, IT management, Еducation with ICT, Eco-informatics, Inteligent Systems, Internet Technologies and cyber security, Computer Science, Software for embedded systems, Software Engineering, Cloud Computing, IT management, Bioinformatics, Security, Cryptography and Coding, Software Engineering, Statistics and Data Analytics, Statistics and Data Analytics,

4.

Organizer of the study program (unit, institute, department, division)

Faculty of Information Sciences and Computer Engineering

5.

Study cycle (first, second, third)

Втор циклус

6.

Academic year / semester

5 / Зимски

7. Number of ECTS credits

6.0

8.

Instructor

9.

Prerequisites for enrollment

10.

Subject goals and competencies:

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.

Subject 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 fund

6.0 ECTS x 30 hours = 180 hours

14.

Time distribution

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

15.

Forms of teaching activities

15.1.

Lectures - theoretical teaching

60 hours

15.2.

Exercises (laboratory, classroom), seminars, team work

0 hours

16.

Other forms of activities

16.1.

Project tasks

45 hours

16.2.

Independent tasks

45 hours

16.3.

Homework

30 hours

17.

Grading method

17.1.

Tests

0 points

17.2.

Seminar work / project (presentation: written and oral)

45 points

17.3.

Activities and learning

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.

Condition for signature and taking final exam

NULL

20.

Language of instruction

македонски

21.

Quality assurance method

интерна евалуација и анкети

22.

Literature

22.1.

Mandatory literature

22.2.

Additional literature