A Dimension Reduction Scheme for the Computation of Optimal Unions of Subspaces

ALDROUBI, AKRAM; ANASTASIO, MAGALI; CABRELLI, CARLOS A.; MOLTER, URSULA M.

Sampling Theory in Signal and Image Processing

Sampling Publishing

Lugar: Potsdam ,NY; Año: 2011 vol. 10 p. 135 - 150

1530-6429

Given a set of points F in a high dimensional space, the problem of finding a union of subspaces ∪i Vi ⊆ R N that best explains the data F increases dramatically with the dimension of RN . 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 approx- imate 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.