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...
| Autores: | , , , |
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| 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 |
| 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 |
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