Optimal data approximation with group invariances
Suppose we are given a finite, typically large, dataset of L^2 functions with domain the Euclidean space or any LCA group, and a semidirectproduct group G of discrete translations and automorphisms/linear applications acting on such a domain. We consider the problem of approximating the dataset by its projection onto the subspace spanned by the action of G on a finite, ideally small, set of functions, called generators. In this seminar, we will first discuss a constructive proof that provides the generators of the optimal subspace for the approximation, and then see the results of this construction on common datasets of natural images. This is a joint work with C. Cabrelli, E. Hernández and U. Molter
Davide Barbieri is an Assistant Professor at Universidad Autónoma de Madrid. He obtained his PhD at Università di Bologna and Université de Cergy Pontoise, and he was a Marie Curie Research Fellow at Universidad Autónoma de Madrid.
2019-10-14 at 2:30 pm (subject to variability)