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: Aldroubi, A., Anastasio, M., Cabrelli, C., Molter, U.
Formato: JOUR
Materias:
Concentration inequalities
Dimensionality reduction
Projective clustering
Random matrices
Sparsity
Acceso en línea: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
Descripción
Sumario: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.

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