Topological data analysis
Section outline
-
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)
-
Uploaded 31/05/17, 14:04
-
Introduction. Basic definitions and concepts: metrics, continuous maps, homeomorphisms, homotopy type.
Textbook: Chapter 1
-
Uploaded 6/10/20, 18:47
-
-
Triangulations in the plane, Voronoi diagram, Delaunay triangulation.
Textbook: Chapter 2
-
Uploaded 4/10/24, 19:37
-
-
Geometric simplicial complexes, Abstract simplicial complexes, Euler characteristic
Textbook: Chapter 3
-
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
Interleaving.
Textbook: Chapter 5
-
Algebraic groups. Intuition and idea of homology.
Textbook: Chapter 6, idea of chapter 7
-
Homology groups
Textbook: Chapters 7 and 8.1
-
Computing homology
Textbook: Chapters 7 and 8.1
-
Persistent homology
Textbook: Chapter 9
-
Filtrations, persistence modules, interleavings, Gromov-Hausdorff distance
Textbook: Chapters 9 and 10
-
Stability theorem for persistent homology, Wasserstein distance, further developments of persistence, examples of applications
Textbook: Chapter 10
-
Write to Santa...
-
Discrete Morse theory: discrete Morse functions, discrete gradient vector fields; Morse chain complex and Morse homology
Textbook: Chapter 11 -
Project presentations