Zhang Yuqian author Columbia University. Electrical Engineering Wright John N. author Columbia University. Electrical Engineering Sun Ju author Columbia University. Electrical Engineering Columbia University. Electrical Engineering originator text Articles 2012 manuscript version English Motivated by vision tasks such as robust face and object recognition, we consider the following general problem: given a collection of low-dimensional linear subspaces in a high-dimensional ambient (image) space, and a query point (image), efficiently determine the nearest subspace to the query in ℓ1 distance. We show in theory this problem can be solved with a simple two-stage algorithm: (1) random Cauchy projection of query and subspaces into low-dimensional spaces followed by efficient distance evaluation (ℓ1 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. Artificial intelligence Computer science Schmid Cordelia editor Sato Yoichi editor Perona Pietro editor Lazebnik Svetlana editor Fitzgibbon Andrew editor New York Springer 2012 416 429 http://dx.doi.org/10.1007/978-3-642-33765-9_30 7575 http://hdl.handle.net/10022/AC:P:14959 NNC NNC 2012-10-16 13:03:07 -0400 2012-10-16 13:11:02 -0400 8963 eng