Learning the Right Model from the Data

In this chapter we discuss the problem of finding the shift-invariant space model that best fits a given class of observed data F. If the data is known to belong to a fixed—but unknown—shift-invariant space V(Φ) generated by a vector function Φ, then we can probe the data F to find out whether the d...

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Detalles Bibliográficos
Autores principales: Aldroubi, A., Cabrelli, C., Molter, U.
Formato: SER
Materias:
Class Versus
Optimal Space
Orthonormal Basis
Riesz Basis
Space Versus
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_22965009_v_n9780817637781_p325_Aldroubi
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_22965009_v_n9780817637781_p325_Aldroubi
record_format dspace
spelling todo:paper_22965009_v_n9780817637781_p325_Aldroubi2023-10-03T16:40:46Z Learning the Right Model from the Data Aldroubi, A. Cabrelli, C. Molter, U. Class Versus Optimal Space Orthonormal Basis Riesz Basis Space Versus In this chapter we discuss the problem of finding the shift-invariant space model that best fits a given class of observed data F. If the data is known to belong to a fixed—but unknown—shift-invariant space V(Φ) generated by a vector function Φ, then we can probe the data F to find out whether the data is sufficiently rich for determining the shift-invariant space. If it is determined that the data is not sufficient to find the underlying shift-invariant space V, then we need to acquire more data. If we cannot acquire more data, then instead we can determine a shift-invariant subspace S ⊂ V whose elements are generated by the data. For the case where the observed data is corrupted by noise, or the data does not belong to a shift-invariant space V(Φ), then we can determine a space V(Φ) that fits the data in some optimal way. This latter case is more realistic and can be useful in applications, e.g., finding a shift-invariant space with a small number of generators that describes the class of chest X-rays. © 2006, Birkhäuser Boston. SER info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_22965009_v_n9780817637781_p325_Aldroubi
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Class Versus
Optimal Space
Orthonormal Basis
Riesz Basis
Space Versus
spellingShingle Class Versus
Optimal Space
Orthonormal Basis
Riesz Basis
Space Versus
Aldroubi, A.
Cabrelli, C.
Molter, U.
Learning the Right Model from the Data
topic_facet Class Versus
Optimal Space
Orthonormal Basis
Riesz Basis
Space Versus
description In this chapter we discuss the problem of finding the shift-invariant space model that best fits a given class of observed data F. If the data is known to belong to a fixed—but unknown—shift-invariant space V(Φ) generated by a vector function Φ, then we can probe the data F to find out whether the data is sufficiently rich for determining the shift-invariant space. If it is determined that the data is not sufficient to find the underlying shift-invariant space V, then we need to acquire more data. If we cannot acquire more data, then instead we can determine a shift-invariant subspace S ⊂ V whose elements are generated by the data. For the case where the observed data is corrupted by noise, or the data does not belong to a shift-invariant space V(Φ), then we can determine a space V(Φ) that fits the data in some optimal way. This latter case is more realistic and can be useful in applications, e.g., finding a shift-invariant space with a small number of generators that describes the class of chest X-rays. © 2006, Birkhäuser Boston.
format SER
author Aldroubi, A.
Cabrelli, C.
Molter, U.
author_facet Aldroubi, A.
Cabrelli, C.
Molter, U.
author_sort Aldroubi, A.
title Learning the Right Model from the Data
title_short Learning the Right Model from the Data
title_full Learning the Right Model from the Data
title_fullStr Learning the Right Model from the Data
title_full_unstemmed Learning the Right Model from the Data
title_sort learning the right model from the data
url http://hdl.handle.net/20.500.12110/paper_22965009_v_n9780817637781_p325_Aldroubi
work_keys_str_mv AT aldroubia learningtherightmodelfromthedata
AT cabrellic learningtherightmodelfromthedata
AT molteru learningtherightmodelfromthedata
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