A general framework for approximate nearest subspace search

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 Approximate Nearest Subspace search problem. Our solution uniformly handles cases where both query and database elements may differ in dimensionality, where the database contains subspaces of different dimensions, and where the queries themselves may be subspaces. 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 performance on synthetic and real data. Our tests indicate that an approximate nearest subspace can be located significantly faster than the nearest subspace, with little loss of accuracy.