Topološka analiza podatkov

Tedenski oris

• General course info
  

  General course info

  Lecturer: 

  • Neža Mramor Kosta (neza.mramor@fri.uni-lj.si)
    

  Assistants: 
  

  • Aleksandra Franc (aleksandra.franc@fri.uni-lj.si)
    
  • Gregor Jerše (gregor.jerse@fri.uni-lj.si)

  • News Forum
  • Questions, answers and discussions Forum
  • Course description - Opis predmeta Stran
  • Student requirements - Obveznosti študentov Stran
  • Lab work - Delo na vajah Stran
  • Literature and other sources Stran
  • Example of a good project report Vir
  • Example 2 of a good project report Vir Naloženo 31/05/2017 14:04
  • 
    

    A topologist is a person, who doesn't know a donut from a coffee cup

    
    

    
    

  • Homework 1

  • Homework results Vir Naloženo 14/05/2018 14:18
  • Project documentation Stran
  • Homework + Projects Results Vir Naloženo 12/06/2018 11:19
  • More exam time slots Možnost
  • Lectures, Part 1 Vir Spremenjeno 26/03/2018 06:12
  • Lectures, Part 2, updated Vir Spremenjeno 21/05/2018 08:08
  • Complete lectures, 2018 Vir Naloženo 12/06/2018 11:38
• 18. februar - 24. februar
  

  18. februar - 24. februar

  Introduction. Basic definitions and concepts: topologies, metrics, continuous maps, homeomorphisms. 

  • Lab work #1 Vir Naloženo 25/02/2018 20:41
• 25. februar - 3. marec
  

  25. februar - 3. marec

  Homeomorphisms

  Plane triangulations, Voronoi diagram, Delaunay triangulation.

  • Lab work #2 Vir Naloženo 1/03/2018 10:38
  • Geogebra URL
• 4. marec - 10. marec
  

  4. marec - 10. marec

  Monday lectures: 

  Properties of the Delauney triangulation. Geometric simplicial complexes, examples

  Friday lectures (instead of next Monday, March 12th when there will be a lab session instead of lectures): 

  Abstract simplicial complexes, examples, links, stars, triangulated surfaces and manifolds. Orientation. Simplicial complexes on data sets: the Vietoris-Rips construction.
• 11. marec - 17. marec
  

  11. marec - 17. marec

  • Lab work: triangulations URL
  • Lab work: surfaces URL
• 18. marec - 24. marec
  

  18. marec - 24. marec

  Triangulated manifolds, orientation. Classification of surfaces.

  Simplicial complexes on data sets:

  • Vietoris Rips complex
  • The nerve construction

  
  

  Levenshtein distance calculator:

  https://planetcalc.com/1721/
  

  • Lab work #5 Vir Naloženo 23/03/2018 10:01
  • Geogebra, problem 3 Vir Naloženo 23/03/2018 10:02
  • Geogebra, problem 6 Vir Naloženo 23/03/2018 10:02
• 25. marec - 31. marec
  

  25. marec - 31. marec

  Homotopy of maps, homotopy equivalence of sets, contractible sets

  Nerve theorem

  
  

  • Lab work: complexes URL
• 1. april - 7. april
  

  1. april - 7. april

  No lectures this Monday, happy Easter!

  • Lab work #7 Vir Naloženo 5/04/2018 21:58
• 8. april - 14. april
  

  8. april - 14. april

  Examples of nerve complexes: Čech,  Delaunay, alpha-shapes

  Towards homology groups: groups, homomphisms, structure theorem for finitely generated abelian groups, quotien groups, chains

  • Lab work resources

  • https://www.projekt-tomo.si/problem_set/1314/ URL
  • bunny points Vir Naloženo 11/04/2018 13:38
  • export triangulation to ply Vir Naloženo 11/04/2018 13:49
  • miniball Vir Naloženo 13/04/2018 10:46
• 15. april - 21. april
  

  15. april - 21. april

  Homology:
  

  • chain complex
  • cycles and boundaries
  • homology groups
  • Betti numbers

  
  

  A nice explanation of the algorithm to compute homology:

  https://jeremykun.com/2013/04/10/computing-homology/
  

  You can also use Dionysus to compute homology (and much more):

  http://www.mrzv.org/software/dionysus/
  

  http://www.mrzv.org/software/dionysus/python/overview.html#python-bindings
  

  Wolfram Demonstration of computing simplicial homology of an alpha complex:

  http://demonstrations.wolfram.com/SimplicialHomologyOfTheAlphaComplex/
  

  Homology with Sage:

  http://doc.sagemath.org/html/en/reference/homology/index.html
  

  Homology (and more) with CHomP:

  http://chomp.rutgers.edu/Software.html
  

  
  

  • Lab work #9 Vir Naloženo 19/04/2018 14:12
  • Lab work #9, solutions Vir Naloženo 19/04/2018 14:37
• 22. april - 28. april
  

  22. april - 28. april

  Computing homology: 

  • matrix representation of boundary homomorphism, reduction to Smith normal form
    
  • reducing the complex: elementary collapses
  • gradient vector fields and Morse homology

  
  
• 29. april - 5. maj
  

  29. april - 5. maj

  Ni na voljo
• 6. maj - 12. maj
  

  6. maj - 12. maj

  Morse homology, algorithm for computing Morse homology, cancelling critical cells

  
  

  • Lab work: computing homology URL
• 13. maj - 19. maj
  

  13. maj - 19. maj

  
  

  • Lab work #11 Vir Naloženo 18/05/2018 10:04
  • Lab work #11, solutions Vir Naloženo 20/05/2018 21:27
• 20. maj - 26. maj
  

  20. maj - 26. maj

  Discrete Morse Theory: 

  Morse functions for data analysis, algorithm for extending sampled values on vertices to a discrete Morse function on the complex

  Sublevel complex filtration, regular events and elementary collapses, critical events 

  Persistence

  Software for computing persistent homology

  • Lab work: Discrete Morse theory (discrete gradient vector field) URL
  • Generating discrete gradient vector field URL
  • Persistent homology Stran
  • Computing persistent homology URL
• 27. maj - 2. junij
  

  27. maj - 2. junij

  Persistence: barcodes, persistence diagrams and persistent homology groups

  Stability of persistence diagrams

  • Lab work #13 Vir Naloženo 1/06/2018 06:57
  • problem 4 (solution) Vir Naloženo 1/06/2018 12:34
• 3. junij - 9. junij
  

  3. junij - 9. junij

  Ni na voljo