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 U_i V_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: Aldroubi, Akram, Anastasio, Magalí, Cabrelli, Carlos, Molter, Ursula Maria
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2011
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/117502
Acceso en línea:http://hdl.handle.net/11336/117502
Access Level:acceso abierto
Palabra clave:SPARSITY
PROJECTIVE CLUSTERING
DIMENSIONALITY REDUCTION
RANDOM MATRICES
CONCENTRATION INEQUALITIES
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario:Given a set of points F in a high dimensional space, the problem of finding a union of subspaces U_i V_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.