Learning optimal smooth invariant subspaces for data approximation
Optimization and Control
2023-11-22 v1 Functional Analysis
Machine Learning
Abstract
In this article, we consider the problem of approximating a finite set of data (usually huge in applications) by invariant subspaces generated through a small set of smooth functions. The invariance is either by translations under a full-rank lattice or through the action of crystallographic groups. Smoothness is ensured by stipulating that the generators belong to a Paley-Wiener space, that is selected in an optimal way based on the characteristics of the given data. To complete our investigation, we analyze the fundamental role played by the lattice in the process of approximation.
Cite
@article{arxiv.2311.12544,
title = {Learning optimal smooth invariant subspaces for data approximation},
author = {Davide Barbieri and Eugenio Hernández and Carlos Cabrelli and Ursula Molter},
journal= {arXiv preprint arXiv:2311.12544},
year = {2023}
}