Topological data analysis
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섹션 개요
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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)
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A topologist is a person, who doesn't know a donut from a coffee cup
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Introduction. Basic definitions and concepts: metrics, continuous maps, homeomorphisms, homotopy type.
Textbook: Chapter 1
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Triangulations in the plane, Voronoi diagram, Delaunay triangulation.
Textbook: Chapter 2
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Geometric simplicial complexes, Abstract simplicial complexes, Euler characteristic
Textbook: Chapter 3
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Triangulated manifolds, orientation. Classification of surfaces.
Textbook: Chapter 4 -
Carve a pumpkin
Simplicial complexes on data sets:
- Vietoris Rips complex
- Cech complex
- The nerve construction
- Mapper
Textbook: Chapter 5
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Fields, vector spaces and their quotients. Intuition, idea, and definition of homology.
Textbook: Chapter 6, idea of chapter 7
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Computing persistent homology
Textbook: Chapter 9