Computational Geometry and Topology for Data Analysis
Jean-Daniel Boissonnat, Frédéric Cazals, Frédéric Chazal, Julien Tierny
January 23-27, 2017 – Inria Sophia Antipolis
This course is an introduction to Computational Geometry and Topology. It will introduce fundamental concepts, data structures and algorithms in this context. It can serve also as an introduction to the emerging field of 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?
- How can we handle noisy data?
- How can we walk around the curse of dimensionality?
Supports de cours:
Geometric and Topological Inference (J-D. Boissonnat, F. Chazal, M. Yvinec)
Introduction to Topological Data Analysis (J. Tierny).
Foundations of Geometric Methods in Data Analysis (F. Cazals)
Module 1: “Algorithmic Geometry of Triangulations”
Jean-Daniel Boissonnat – Datashape, Inria Sophia Antipolis
- “Polytopes, Tesselations and Triangulations”
- “Randomized Algorithms “
- “Quality of Delaunay Complexes”
- “Triangulation of Manifolds”
Module 2: “An Introduction to Topological Data Analysis Through Persistent Homology”
Frédéric Chazal – Datashape, Inria Saclay
- “Covers and nerves: union of balls, geometric inference and exploratory topological data analysis”
- “Homology: introduction and inference from point cloud data”
- “Persistent homology for functions and point clouds”
- “Applications in Topological Data Analysis: clustering and multiscale topological signatures”
Module 3: “Topological and Geometrical Analysis of 3D Data for Scientific Visualization”
Julien Tierny – UPMC.
Module 4: “Nearest Neighbors Algorithms in Euclidean and Metric Spaces: Algorithms and Data Structures”
Frédéric Cazals – ABS, Inria Sophia Antipolis
Talks:
Karthik C. S. – Weizmann Institute of Science – “An Efficient Representation for Filtrations of Simplicial Complexes”
Clément Maria – University of Queensland – “Algorithms to Compute Persistent Homology”
Mael Rouxel-Labbé – Geometry Factory – “Anisotropic Mesh Generation”
Program:
Registration:
Please fill in the registration form and send it by email to florence.barbara@inria.fr
Practical informations:
Place:
Inria Sophia Antipolis
2004 Route des Lucioles
06902 Sophia Antipolis
How to reach Inria Sophia
Accommodation:
Some student rooms have been booked at CIV Valbonne for Master’s students from ENS Lyon from sunday evening till friday morning, on a first-come, first-served basis. If you want to book a room at CIV, please complete the field in the registration form.
Lunch:
Students will have the possibility to have lunch at the university canteen on presentation of their student card.
