Learning optimal smooth invariant subspaces for data approximation

In this article, we consider the problem of approximating a finite set of data (usually huge in applications) by invariant subspaces generated by a small set of smooth functions. The invariance is either by translations under a full-rank lattice or through the action of crystallographic groups. Smoo...

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Detalles Bibliográficos
Autores: Barbieri, Davide, Cabrelli, Carlos, Hernández Rodríguez, Eugenio, Molter, U.
Tipo de recurso: artículo
Fecha de publicación:2024
País:España
Institución:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/712060
Acceso en línea:http://hdl.handle.net/10486/712060
https://dx.doi.org/10.1016/j.jmaa.2024.128348
Access Level:acceso abierto
Palabra clave:Paley-Wiener spaces
Data Approximation
Invariant Subspaces
Optimal Subspaces
Paley-Wiener Spaces
Matemáticas
Descripción
Sumario:In this article, we consider the problem of approximating a finite set of data (usually huge in applications) by invariant subspaces generated by 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, which 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