Kantorovich-Wasserstein metric and clustering of histograms and images
A hacking day of Mathematics for Data Science at the Department of Mathematics
 |
|
Bio
Federico Bassetti is associate professor of probability and mathematical statistics at Politecnico di Milano. He received his PhD in mathematical statistics from the university of Pavia in 2005. From 2006 to 2017 he was assistant professor and subsequently associate professor in the university of Pavia. His main research activity focuses on bayesian statistics with application to biology and econometry and limit theorems in probability, especially for Kac like equations. He is also interested in random graphs and interacting particle systems.Abstract
The Kantorovich-Wasserstein metric has been successfully used in several branches of mathematics, including probability, analysis and statistics. It has recently found applications also in computer science, machine learning and image processing. The goal of this lecture is to provide an overview on applications of probability metrics and, specifically, of the Kantorovich-Wasserstein distance. In particular we will focus on the problem of clustering discrete distributions and its application to statistics and image processing.
Tentative topics: The Wasserstein distance on the real line and the Hitchcock-Koopmans transportation problem. Flow on graphs and optimal transport in discrete settings. Computational issues. Application to clustering of images and histograms.
References
- Peyré, Gabriel, and Marco Cuturi. Computational optimal transport. Foundations and Trends in Machine Learning 11.5-6 (2019): 355-607.
Schedule
- Monday 2019/12/02 10:30 - 13.15 Room A213
Details
- The participation is free. Please send an email to Prof. Claudio Agostinelli.
- For further information, please contact Prof. Claudio Agostinelli
- Poster: PDF
- Venue: Polo Scientifico e Tecnologico F. Ferrari – Room A213
- Language: English