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Content and learning outcomes
The course contains the following topics:
- Kleinberg theorem about impossibility of clustering,
- metric spaces and dendrograms,
- classical hierarchical clustering schemes (single, complete, average, and Haussdorff linkage),
- elements of simplicial complexes,
- transforming data into simplicial complexes via Chech and Vietoris-Rips constructions
- extracting homology out of data based simplicial complexes
- persistence modules, barcoding, and feature visualization
Intended learning outcomes
After completing the course, the student shall be able to
- use concepts, propositions and methods to solve, and present the solution of problems within topological data analysis;
- use available software to analyze geometric data.
Literature and preparations
- English B / English 6
- Completed basic course in numerical analysis (SF1544, SF1545 or equivalent)
- Completed basic course in probability theory and statistics (SF1922, SF1914 or equivalent)
Completed courses corresponding to SF2935 Modern methods of statistical learning and SF2940 Probability theory.
Various books and lecture notes presented on the course web page.
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
- PRO1 - Project, 7.5 credits, grading scale: A, B, C, D, E, FX, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
Opportunity to complete the requirements via supplementary examination
Opportunity to raise an approved grade via renewed examination
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.
Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.Course web SF2956