info:eu-repo/semantics/article
A dimension reduction scheme for the computation of optimal unions of subspaces
Date
2011-11Registration in:
Aldroubi, Akram; Anastasio, Magalí; Cabrelli, Carlos; Molter, Ursula Maria; A dimension reduction scheme for the computation of optimal unions of subspaces; Sampling Publishing; Sampling Theory in Signal and Image Processing; 10; 1-2; 11-2011; 135-150
1530-6429
CONICET Digital
CONICET
Author
Aldroubi, Akram
Anastasio, Magalí
Cabrelli, Carlos
Molter, Ursula Maria
Abstract
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.