Issue No. 02 - February (2011 vol. 33)
Ronen Basri , Weizmann Institute of Science, Rehovot
Tal Hassner , The Open University of Israel, Raanana
Lihi Zelnik-Manor , The Technion–Israel Institute of Technology, Haifa
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.
Approximate nearest neighbor search techniques, subspace representations.
L. Zelnik-Manor, R. Basri and T. Hassner, "Approximate Nearest Subspace Search," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 33, no. , pp. 266-278, 2010.