Learning optimal smooth invariant subspaces for data approximation

• Published in: Journal of mathematical analysis and applications Vol. 538; no. 2; p. 128348
• Main Authors: Barbieri, D., Cabrelli, C., Hernández, E., Molter, U.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15-10-2024
• Subjects: Data approximation; Invariant subspaces; Optimal subspaces; Paley-Wiener spaces; Invariant subspaces; Paley-Wiener spaces; Optimal subspaces; Data approximation
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2024.128348

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.