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Finding the nearest subspace is a fundamental problem and influential to manyapplications. In particular, a scalable solution that is fast and accurate fora large problem has a great impact. The existing methods for the problem are,however, useless in a large-scale problem with a large number of subspaces andhigh dimensionality of the feature space. A cause is that they are designedbased on the traditional idea to represent a subspace by a single point. Inthis paper, we propose a scalable solution for the approximate nearest subspacesearch (ANSS) problem. Intuitively, the proposed method represents a subspaceby multiple points unlike the existing methods. This makes a large-scale ANSSproblem tractable. In the experiment with 3036 subspaces in the1024-dimensional space, we confirmed that the proposed method was 7.3 timesfaster than the previous state-of-the-art without loss of accuracy.

Scalable Solution for Approximate Nearest Subspace Search