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

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

2010-08-17

arxiv.org/abs/1008.2804v2

Mathematics

Classical Analysis and ODEs

15 pages. Some corrections were added, in particular the title was changed. It will appear in "Sampling Theory in Signal and I

Scientific paper

Given a set of points \F in a high dimensional space, the problem of finding a union of subspaces \cup_i V_i\subset \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.

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