Computational Geometry and Topology for Data Analysis
Jean-Daniel Boissonnat, Frédéric Chazal, Kunal Dutta, Alfredo Hubard
January 11-15, 2016 – INRIA Sophia Antipolis
This course is an introduction to the emerging field of Geometric and Topological Data Analysis. Fundamental questions to be addressed are:
– How can we represent complex shapes in high-dimensional spaces ?
– How can we infer properties of shapes from samples even in the presence of noise ?
Module 1: “Algorithmic Geometry of Triangulations” – Course Notes
- Simplicial complexes in metric spaces
- Delaunay complexes, Voronoi diagrams and convex hulls, Union of balls and a-complexes
- Witness Complexes
Module 2: “An Introduction to Topological Data Analysis Through Persistent Homology”
Frédéric Chazal – Slides 1 – Slides 2
- Homology: introduction and inference from point cloud data.
- Persistent homology for functions and point clouds.
- Applications in TDA: clustering and multiscale topological signatures.
Module 3: “Computational Convexity and Isoperimetry”
Alfredo Hubard
- Combinatorial convexity and big data.
- Volumes in convex bodies.
- Separators in graphs and expander graphs
Module 4: “”
Kunal Dutta
- Introduction to VC-dimension, -Nets, and -Samples
- Introduction to Combinatorial Discrepancy
- Haussler’s Packing Lemma
- Primal and Dual Shatter Dimensions, and -Nets for Geomtric Set Systems
- Shallow Packing, Weighted -Nets, and Quasi-random Sampling
Program:
Registration:
For organisational reasons, if you wish to attend the winter school, please send a mail to florence.barbara@inria.fr before January 4th. This will also allow us to warn you about changes in the organisation if necessary.
Practical information:
Place:
Inria Sophia Antipolis
Building Kahn – Room K2-K3
2004 Route des Lucioles
06902 Sophia Antipolis
How to reach Inria Sophia
Accommodation:
INRIA offers to accommodate Master’s students at CIV Valbonne (from January 10th to 15th). The number of places being limited, we recommend that you complete the accommodation form as soon as possible.
Lunch:
Students will have the possibility to have lunch at the university canteen on presentation of their student card.
