Abstract

Motivated by vision tasks such as robust face and ob ject recognition, we consider the following general problem: given a collec- tion of low-dimensional linear subspaces in a high-dimensional ambient (image) space, and a query point (image), efficiently determine the near- est subspace to the query in *1 distance. We show in theory this problem can be solved with a simple two-stage algorithm: (1) random Cauchy pro- jection of query and subspaces into low-dimensional spaces followed by efficient distance evaluation (*1 regression); (2) getting back to the high- dimensional space with very few candidates and performing exhaustive search. We present preliminary experiments on robust face recognition to corroborate our theory.