Topological data analysis

Section outline

• Select section General course info

  General course info

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  Lecturer: 

  • Žiga Virk (ziga.virk@fri.uni-lj.si)

  Assistants:

  • Aleksandra Franc (aleksandra.franc@fri.uni-lj.si)
  • Damir Franetič (damir.franetic@fri.uni-lj.si)

  • Select activity News

    

    News Forum
  • Select activity Questions, answers and discussions

    

    Questions, answers and discussions Forum
  • Select activity Course description - Opis predmeta

    

    Course description - Opis predmeta Page
  • Select activity Student requirements - Obveznosti študentov

    

    Student requirements - Obveznosti študentov Page
  • Select activity Lab work - Delo na vajah

    

    Lab work - Delo na vajah Page
  • Select activity Literature and other sources

    

    Literature and other sources Page
  • Select activity Julia, VS Code & Jupyter

    

    Julia, VS Code & Jupyter Page
  • Select activity Julia Cheatsheet

    

    Julia Cheatsheet URL
  • Select activity Example of a good project report

    

    Example of a good project report File
  • Select activity Example 2 of a good project report

    

    Example 2 of a good project report File

    Uploaded 31/05/17, 14:04
  • Select activity A topologist is a person, who doesn't know a donut...

    
    

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

    
    

    
    

  • Select activity Homework

    Homework

  • Select activity HW1 Dropbox

    

    HW1 Dropbox Assignment
  • Select activity HW2 Dropbox

    

    HW2 Dropbox Assignment
  • Select activity HW3 Dropbox

    

    HW3 Dropbox Assignment
  • Select activity Group Project

    Group Project

  • Select activity Group Project Dropbox

    

    Group Project Dropbox Assignment
  • Select activity Project assignment documentation

    

    Project assignment documentation Page
• Select section 30 September - 6 October

  30 September - 6 October

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

  Textbook: Chapter 1

  • Select activity Notes, lecture 1

    

    Notes, lecture 1 File

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  • Select activity There is no difference between a donut and a coffee cup ...

    

    There is no difference between a donut and a coffee cup ... URL
  • Select activity Topology and topological data analysis (from AYASDI)

    

    Topology and topological data analysis (from AYASDI) URL
  • Select activity The intuition behind topology

    

    The intuition behind topology Page
• Select section 7 October - 13 October

  7 October - 13 October

  Triangulations in the plane, Voronoi diagram, Delaunay triangulation.
  

  Textbook: Chapter 2
  

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    Notes, lecture 2 File

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    Lab work, 2nd week File

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• Select section 14 October - 20 October

  14 October - 20 October

  Geometric simplicial complexes, Abstract simplicial complexes, Euler characteristic

  Textbook: Chapter 3
  

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    Notes, lecture 3 File

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  • Select activity Lab work #3

    

    Lab work #3 File

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  • Select activity Cool links (Klein Bottle)

    

    Cool links (Klein Bottle) URL
  • Select activity Cool links (Voronoi diagrams)

    

    Cool links (Voronoi diagrams) Page
  • Select activity Cool links (Homotopy)

    

    Cool links (Homotopy) URL
  • Select activity Cool links (Simplices)

    

    Cool links (Simplices) URL
  • Select activity Cool links (The Sound of the Moebius Strip)

    

    Cool links (The Sound of the Moebius Strip) URL
• Select section 21 October - 27 October

  21 October - 27 October

  Triangulated manifolds, orientation. Classification of surfaces.
  
  Textbook: Chapter 4
  

  • Select activity Notes, lecture 4

    

    Notes, lecture 4 File

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  • Select activity Lab work #4

    

    Lab work #4 File
  • Select activity Lab work #4 Jupyter Notebook

    

    Lab work #4 Jupyter Notebook File
  • Select activity line_sweep.jl (Julia file)

    

    line_sweep.jl (Julia file)
  • Select activity line_sweep.ipnyb (Jupyter Notebook, improvements and alternative approaches)

    

    line_sweep.ipnyb (Jupyter Notebook, improvements and alternative approaches) File
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    HTML of the above File
• Select section 28 October - 3 November

  28 October - 3 November

  Carve a pumpkin
  
• Select section 4 November - 10 November

  4 November - 10 November

  Simplicial complexes on data sets:
  

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

  Interleaving.

  Textbook: Chapter 5
  

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    Notes, lecture 5 File

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    Lab work #5 (Jupyter Notebook, to be opened locally) File

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  • Select activity basic_scx.jl (basic constructions with abstract simplicial complexes, a Julia file)

    

    basic_scx.jl (basic constructions with abstract simplicial complexes, a Julia file)

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• Select section 11 November - 17 November

  11 November - 17 November

  Algebraic groups. Intuition and idea of homology.
  

  Textbook: Chapter 6, idea of chapter 7
  

  
  

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    Notes, Lecture 6 File

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  • Select activity Voronoi game

    

    Voronoi game URL
  • Select activity Lab work, 6th week

    

    Lab work, 6th week File

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    Geogebra URL
• Select section 18 November - 24 November

  18 November - 24 November

  Homology groups

  Textbook: Chapters 7 and 8.1
  

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    Notes, Lecture 7 File

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    Lab work, 7th week File

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• Select section 25 November - 1 December

  25 November - 1 December

  Computing homology

  Textbook: Chapters 7 and 8.1
  

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    Notes, Lectures 7 & 8 File

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    Lab work, 8th week File

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• Select section 2 December - 8 December

  2 December - 8 December

  Persistent homology

  Textbook: Chapter 9

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    Notes, lectures 9 File

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    Lab work #9 (Jupyter Notebook, to be opened locally) File

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  • Select activity simplicial_homology.jl (Julia file with complete functions for the above.)

    

    simplicial_homology.jl (Julia file with complete functions for the above.)

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• Select section 9 December - 15 December

  9 December - 15 December

  Filtrations, persistence modules, interleavings, Gromov-Hausdorff distance
  

  Textbook: Chapters 9 and 10
  

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    Notes, Lectures 10-11 File

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    Lab work #10 File

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• Select section 16 December - 22 December

  16 December - 22 December

  Stability theorem for persistent homology, Wasserstein distance, further developments of persistence, examples of applications

  Textbook: Chapter 10
  

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    Lab work #11 File

    Modified 16/12/24, 14:14
  • Select activity Optional lab work #11 (programming your own 'persistent homology' ...)

    

    Optional lab work #11 (programming your own 'persistent homology' ...) File

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• Select section 23 December - 29 December

  23 December - 29 December

  Write to Santa...

  • Select activity Lab work #12 (Jupyter Notebook, to be opened locally)

    

    Lab work #12 (Jupyter Notebook, to be opened locally) File

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• Select section 30 December - 5 January

  30 December - 5 January
• Select section 6 January - 12 January

  6 January - 12 January

  Discrete Morse theory: discrete Morse functions, discrete gradient vector fields; Morse chain complex and Morse homology
  
  Textbook: Chapter 11

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    Notes Discrete Morse Theory File

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• Select section 13 January - 19 January

  13 January - 19 January

  Lab work, twice (discrete Morse theory - Tuesday and/or Friday, distance between persistence diagrams - Wednesday)

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    Lab work #13 File

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    Lab work #14 File

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• Select section 20 January - 26 January

  20 January - 26 January

  Not available