Approximate Nearest Subspace Search

Published in IEEE Trans. on Pattern Analysis and Machine Intelligence (TPAMI), 33(2), 2011

Recommended citation: Ronen Basri, Tal Hassner, and Lihi Zelnik-Manor*. Approximate Nearest Subspace Search; IEEE Trans. on Pattern Analysis and Machine Intelligence (TPAMI), 33(2), 2011

Image reconstruction results. Reconstructed using a single outdoor scene image

Image reconstruction details. (a) The single database image used for reconstruction, (b) mean runtimes for each method, and (c) L1 error reconstruction error for each of the test images. Both database and query images were taken from the Corel data set.


Subspaces offer convenient means of representing information in many pattern recognition, machine vision, and statistical learning applications. Contrary to the growing popularity of subspace representations, the problem of efficiently searching through large subspace databases has received little attention in the past. In this paper, we present a general solution to the problem of Approximate Nearest Subspace search. Our solution uniformly handles cases where the queries are points or subspaces, where query and database elements differ in dimensionality, and where the database contains subspaces of different dimensions. To this end, we present a simple mapping from subspaces to points, thus reducing the problem to the well-studied Approximate Nearest Neighbor problem on points. We provide theoretical proofs of correctness and error bounds of our construction and demonstrate its capabilities on synthetic and real data. Our experiments indicate that an approximate nearest subspace can be located significantly faster than the nearest subspace, with little loss of accuracy.

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