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Given a set of points \F in a high dimensional space, the problem of findinga union of subspaces \cup_i V_i\subset \R^N that best explains the data \Fincreases dramatically with the dimension of \R^N. In this article, we study aclass of transformations that map the problem into another one in lowerdimension. We use the best model in the low dimensional space to approximatethe best solution in the original high dimensional space. We then estimate theerror produced between this solution and the optimal solution in the highdimensional space.

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