Topological data analysis

Weekly outline

• 

  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
  • Oral exams Zoom meeting
  • Example of a good project report File
  • Example 2 of a good project report File Uploaded 31/05/17, 14:04
  • 
    

    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
  • export triangulation to ply File Uploaded 11/04/18, 13:49
  • Group Project

  • Group Project Dropbox Assignment
  • Presentation schedule Page
  • Project documentation Page
• 

  5 October - 11 October

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

  • Lecture 1, part 1 URL
  • Lecture 1, part 2 URL
  • Lecture 1, part 3 URL
  • Lecture 1, part 4 URL
  • Notes, lecture 1 File Uploaded 6/10/20, 18:47
  • Why there is no difference between a donut and a coffee cup ... URL
  • Topology and topological data analysis (from AYASDI) URL
  • Lab work #1 File Uploaded 14/10/20, 11:07
• 

  12 October - 18 October

  Triangulations in the plane, Voronoi diagram, Delaunay triangulation.
  

  • Lecture 2, part 1 URL
  • Lecture 2, part 2 URL
  • Lecture 2, part 3 URL
  • Notes, lecture 2 File Uploaded 14/10/20, 09:43
  • Lab work #2 File Uploaded 14/10/20, 11:07
  • Voronoi diagram game URL
  • Voronoi diagrams and football URL
  • Geogebra URL
  • Herbert Edelsbrunner: Lecture notes on Delaunay triangulations URL
• 

  19 October - 25 October

  Geometric simplicial complexes, Abstract simplicial complexes, Euler characteristic

  • Lecture 3, part 1 URL
  • Lecture 3, part 2 URL
  • Lecture 3, part 3 URL
  • Notes, lecture 3 File Uploaded 20/10/20, 15:04
• 

  26 October - 1 November

  Triangulated manifolds, orientation. Classification of surfaces.

  • Lecture 4, part 1 URL
  • Lecture 4, part 2 URL
  • Lecture 4, part 3 URL
  • Notes, lecture 4 File Uploaded 27/10/20, 15:41
  • Data for Lab 4 File Uploaded 12/03/17, 19:16
  • Lab work #4 File Uploaded 27/10/20, 19:15
• 

  2 November - 8 November

  Simplicial complexes on data sets:
  

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

  Interleaving.

  • Lecture 5, part 1 URL
  • Lecture 5, part 2 URL
  • Lecture 5, part 3 URL
  • Notes, lecture 5 File Uploaded 3/11/20, 16:41
• 

  9 November - 15 November

  Algebraic groups. Intuition and idea of homology.
  

  
  

  • Lecture 6, part 1 URL
  • Lecture 6, part 2 URL
  • Lecture 6, part 3 URL
  • Notes, Lecture 6 File Uploaded 10/11/20, 15:17
• 

  16 November - 22 November

  Homology groups

  • Lecture 7, part 2 URL
  • Lectures 7, part 3 URL
  • Notes, Lecture 7 File Uploaded 17/11/20, 15:31
  • Lab work #7 File Uploaded 16/11/20, 16:26
• 

  23 November - 29 November

  Computing homology

  • Lecture 8, part 1 URL
  • Lecture 8, part 2 URL
  • Lecture 8, part 3 URL
  • Notes, Lectures 7 & 8 File Uploaded 24/11/20, 15:14
  • Lab work resources

  • Lab work #8 File Uploaded 24/11/20, 22:26
  • Computing homology in Python Page
  • Whiteboard scribbles #8 File Uploaded 25/11/20, 11:05
• 

  30 November - 6 December

  Persistent homology

  Notes, Lecture 9

  You can 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
• 

  7 December - 13 December

  Persistence diagrams: examples, stability

  Lectures, Part 1 

   

  Lectures, Part 2 

  Lectures, Part 3 

  Notes, Leture 10

  
  
• 

  14 December - 20 December

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

  • Lab work #11 File Uploaded 15/12/20, 16:27
  • Whiteboard scribbles #11 File Uploaded 16/12/20, 12:44
  • Lectures, Part 1 URL

    Persistence: stability

  • Lectures, Part 2 URL

    Discrete Morse theory: discrete Morse functions, discrete vector fields

  • Lectures, Part 3 URL

    Discrete Morse theory: sublevel complexes

  • Notes File Uploaded 17/12/20, 10:36
• 

  21 December - 27 December

  Morse homology

  
  

  • Lab work #12 File Uploaded 22/12/20, 16:13
  • Lab work, additional problems and solutions File Uploaded 22/12/20, 23:08
  • Whiteboard scribbles #12 File Uploaded 23/12/20, 11:15
  • Notes File Uploaded 4/01/21, 18:43
• 

  28 December - 3 January

  No school this week:)

  Happy New Year!!
• 

  4 January - 10 January

  Discrete Morse theory: algorithms 

  Software for computing persistent homology
• 

  11 January - 17 January

  Project presentations: Tuesday, 12-15
• This week
  

  18 January - 24 January

  Not available