A dimension reduction scheme for the computation of optimal unions of subspaces

Given a set of points F in a high dimensional space, the problem of finding a union of subspaces ∪ iV i ⊆ ℝ N that best explains the data F increases dramatically with the dimension of ℝ N. In this article, we study a class of transformations that map the problem into another one in lower dimension....

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Detalles Bibliográficos
Autores principales:	Anastasio, Magalí, Cabrelli, Carlos Alberto, Molter, Ursula Maria
Publicado:	2011
Materias:	Concentration inequalities Dimensionality reduction Projective clustering Random matrices Sparsity
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15306429_v10_n1-2_p135_Aldroubi http://hdl.handle.net/20.500.12110/paper_15306429_v10_n1-2_p135_Aldroubi
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_15306429_v10_n1-2_p135_Aldroubi
record_format	dspace
spelling	paper:paper_15306429_v10_n1-2_p135_Aldroubi2023-06-08T16:19:44Z A dimension reduction scheme for the computation of optimal unions of subspaces Anastasio, Magalí Cabrelli, Carlos Alberto Molter, Ursula Maria Concentration inequalities Dimensionality reduction Projective clustering Random matrices Sparsity Given a set of points F in a high dimensional space, the problem of finding a union of subspaces ∪ iV i ⊆ ℝ N that best explains the data F increases dramatically with the dimension of ℝ N. In this article, we study a class of transformations that map the problem into another one in lower dimension. We use the best model in the low dimensional space to approximate the best solution in the original high dimensional space. We then estimate the error produced between this solution and the optimal solution in the high dimensional space. © 2011 SAMPLING PUBLISHING. Fil:Anastasio, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Cabrelli, C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Molter, U. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2011 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15306429_v10_n1-2_p135_Aldroubi http://hdl.handle.net/20.500.12110/paper_15306429_v10_n1-2_p135_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	Concentration inequalities Dimensionality reduction Projective clustering Random matrices Sparsity
spellingShingle	Concentration inequalities Dimensionality reduction Projective clustering Random matrices Sparsity Anastasio, Magalí Cabrelli, Carlos Alberto Molter, Ursula Maria A dimension reduction scheme for the computation of optimal unions of subspaces
topic_facet	Concentration inequalities Dimensionality reduction Projective clustering Random matrices Sparsity
description	Given a set of points F in a high dimensional space, the problem of finding a union of subspaces ∪ iV i ⊆ ℝ N that best explains the data F increases dramatically with the dimension of ℝ N. In this article, we study a class of transformations that map the problem into another one in lower dimension. We use the best model in the low dimensional space to approximate the best solution in the original high dimensional space. We then estimate the error produced between this solution and the optimal solution in the high dimensional space. © 2011 SAMPLING PUBLISHING.
author	Anastasio, Magalí Cabrelli, Carlos Alberto Molter, Ursula Maria
author_facet	Anastasio, Magalí Cabrelli, Carlos Alberto Molter, Ursula Maria
author_sort	Anastasio, Magalí
title	A dimension reduction scheme for the computation of optimal unions of subspaces
title_short	A dimension reduction scheme for the computation of optimal unions of subspaces
title_full	A dimension reduction scheme for the computation of optimal unions of subspaces
title_fullStr	A dimension reduction scheme for the computation of optimal unions of subspaces
title_full_unstemmed	A dimension reduction scheme for the computation of optimal unions of subspaces
title_sort	dimension reduction scheme for the computation of optimal unions of subspaces
publishDate	2011
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15306429_v10_n1-2_p135_Aldroubi http://hdl.handle.net/20.500.12110/paper_15306429_v10_n1-2_p135_Aldroubi
work_keys_str_mv	AT anastasiomagali adimensionreductionschemeforthecomputationofoptimalunionsofsubspaces AT cabrellicarlosalberto adimensionreductionschemeforthecomputationofoptimalunionsofsubspaces AT molterursulamaria adimensionreductionschemeforthecomputationofoptimalunionsofsubspaces AT anastasiomagali dimensionreductionschemeforthecomputationofoptimalunionsofsubspaces AT cabrellicarlosalberto dimensionreductionschemeforthecomputationofoptimalunionsofsubspaces AT molterursulamaria dimensionreductionschemeforthecomputationofoptimalunionsofsubspaces
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A dimension reduction scheme for the computation of optimal unions of subspaces

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