Approximate nearest subspace search

Ronen Basri, Tal Hassner, Lihi Zelnik-Manor

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number5477422
Pages (from-to)266-278
Number of pages13
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number2
StatePublished - 2011

Bibliographical note

Funding Information:
The research of Lihi Zelnik-Manor is supported by Marie Curie IRG-208529. The vision group at the Weizmann Institute is supported in part by the Moross Foundation. This research was performed partly while Ronen Basri was at the Toyota Technological Institute at Chicago. This manuscript contains results that have previously appeared in the Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2007) [5] and the Proceedings of the International Workshop on Subspace Methods at the IEEE International Conference on Computer Vision (ICCV) (2009) [6]. Author names in alphabetical order due to equal contribution.


  • Approximate nearest neighbor search techniques
  • subspace representations.


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