Efficient point-to-subspace query in ℓ1 with application to robust face recognition

Authors:
Ju Sun;Yuqian Zhang;John Wright
Affiliations:
Department of Electrical Engineering, Columbia University, New York;Department of Electrical Engineering, Columbia University, New York;Department of Electrical Engineering, Columbia University, New York
Venue:
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part IV
Year:
2012

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Abstract

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.