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Motivated by vision tasks such as robust face and object recognition, weconsider the following general problem: given a collection of low-dimensionallinear subspaces in a high-dimensional ambient (image) space and a query point(image), efficiently determine the nearest subspace to the query in $\ell^1$distance. We show in theory that Cauchy random embedding of the objects intosignificantly-lower-dimensional spaces helps preserve the identity of thenearest subspace with constant probability. This offers the possibility ofefficiently selecting several candidates for accurate search. We sketchpreliminary experiments on robust face and digit recognition to corroborate ourtheory.

Efficient Point-to-Subspace Query in $\ell^1$: Theory and Applications in Computer Vision