Topological data analysis

Weekly outline

• General course info
  

  General course info

  Lecturers: 

  • Neža Mramor Kosta (neza.mramor@fri.uni-lj.si)
    
  • Žiga Virk (ziga.virk@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 Page
  • Student requirements - Obveznosti študentov Page
  • Lab work - Delo na vajah Page
  • Literature and other sources Page
  • Example of a good project report File
  • Example 2 of a good project report File Uploaded 31/05/17, 14:04
  • Complete (more or less) lectures 2017 File
  • Lecture 1 File Uploaded 13/01/20, 12:05
  • Lecture 2 File Uploaded 13/01/20, 12:05
  • Lecture 3 File Uploaded 13/01/20, 12:05
  • Lecture 4 File Uploaded 13/01/20, 12:05
  • 
    

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

    
    

    
    

  • Homework 1

  • HW1 Dropbox Assignment
  • Homework 2

  • HW2 Dropbox Assignment
  • Homework 3

  • HW3 Dropbox Assignment
  • Group Project

  • Project documentation Page
  • Group Project Dropbox Assignment
  • Presentation schedule Page
  • How to generate uniformly random points on n-spheres and n-balls URL
  • Evenly distributing points on a sphere URL
  • Evenly Distributing Points in a Triangle URL
  • Generating equidistant points URL
• 7 October - 13 October
  

  7 October - 13 October

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

  • Lab work #1 File Uploaded 8/10/19, 15:35
  • Lab work #1 - some solutions File Uploaded 10/10/19, 15:06
  • Why there is no difference between a donut and a coffee cup ... URL
  • Topological analysis on basketball data URL
  • Topology and topological data analysis (from AYASDI) URL
• 14 October - 20 October
  

  14 October - 20 October

  Triangulations in the plane, Voronoi diagram, Delaunay triangulation.
  

  • Lab work #2 File Uploaded 16/10/19, 11:05
  • Geogebra URL
  • Example of a cyclic quadrilateral in Geogebra File Uploaded 5/03/19, 13:06
  • Voronoi diagram game URL
• 21 October - 27 October
  

  21 October - 27 October

  Geometric simplicial complexes, Abstract simplicial complexes, Euler characteristic
• 28 October - 3 November
  

  28 October - 3 November

  Triangulated manifolds, orientation. Classification of surfaces.
• 4 November - 10 November
  

  4 November - 10 November

  Simplicial complexes on data sets:
  

  • Vietoris Rips complex
  • Cech complex
  • The nerve construction
  • Mapper

  
  

  Levenshtein distance calculator:

  https://planetcalc.com/1721/
  
• 11 November - 17 November
  

  11 November - 17 November

  Interleaving. Algebraic groups. Intuition and idea of homology.
  

  
  

  • Lab work #5 File Uploaded 14/11/19, 07:32
  • Geogebra, problem 5-3 File Uploaded 13/11/19, 11:12
  • Geogebra, problem 5-6 File Uploaded 13/11/19, 11:13
  • Geogebra URL
• 18 November - 24 November
  

  18 November - 24 November

  Homology groups

  • bunny points File Uploaded 11/04/18, 13:38
• 25 November - 1 December
  

  25 November - 1 December

  Computing homology

  • Lab work #7 File Uploaded 27/11/19, 14:32
  • Lab work resources

• 2 December - 8 December
  

  2 December - 8 December

  Persistent homology

  
  

  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
  

  
  

  • Computing homology using Dionysus (example) URL
  • Lab work #8 File Uploaded 4/12/19, 20:11
• 9 December - 15 December
  

  9 December - 15 December

  Persistent homology: bar codes, persistence diagrams

  
  
• 16 December - 22 December
  

  16 December - 22 December

  Discrete Morse theory: discrete Morse functions, discrete gradient vector fields, Morse chain complex and Morse homology

  • Lab work #11 File Uploaded 14/12/19, 20:35
• 23 December - 29 December
  

  23 December - 29 December

  Not available
• 30 December - 5 January
  

  30 December - 5 January

  No school this week:)

  Happy New Year!!
• 6 January - 12 January
  

  6 January - 12 January

  Not available
• 13 January - 19 January
  

  13 January - 19 January

  Not available
• 20 January - 26 January
  

  20 January - 26 January

  Not available