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

Sampl. Publ.

Lugar: Potsdam; 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 $cup_i V_isubset R^N$ 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.