Topological data analysis
Section outline
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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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Uploaded 31/05/17, 14:04
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Introduction. Basic definitions and concepts: metrics, continuous maps, homeomorphisms, homotopy type.
Textbook: Chapter 1
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Uploaded 6/10/20, 18:47
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Triangulations in the plane, Voronoi diagram, Delaunay triangulation.
Textbook: Chapter 2
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Uploaded 14/10/20, 09:43
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Uploaded 4/10/24, 19:37
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Geometric simplicial complexes, Abstract simplicial complexes, Euler characteristic
Textbook: Chapter 3
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Uploaded 20/10/20, 15:04
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Uploaded 13/10/24, 11:03
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Triangulated manifolds, orientation. Classification of surfaces.
Textbook: Chapter 4-
Uploaded 27/10/20, 15:41
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Carve a pumpkin
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Simplicial complexes on data sets:
- Vietoris Rips complex
- Cech complex
- The nerve construction
- Mapper
Interleaving.
Textbook: Chapter 5
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Uploaded 3/11/20, 16:41
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Algebraic groups. Intuition and idea of homology.
Textbook: Chapter 6, idea of chapter 7
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Uploaded 10/11/20, 15:17
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Homology groups
Textbook: Chapters 7 and 8.1
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Uploaded 17/11/20, 15:31
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Computing homology
Textbook: Chapters 7 and 8.1
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Uploaded 24/11/20, 15:14
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Persistent homology
Textbook: Chapter 9
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Uploaded 7/11/23, 18:59
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Stability theorem for persistent homology, Wasserstein distance, further developments of persistence, examples of applications
Textbook: Chapter 10
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Write to Santa...
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Discrete Morse theory: discrete Morse functions, discrete gradient vector fields; Morse chain complex and Morse homology
Textbook: Chapter 11-
Uploaded 7/11/23, 19:01
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