  Binary Hashing is widely used for effective approximate nearest neighbors
search. Even though various binary hashing methods have been proposed, very few
methods are feasible for extremely high-dimensional features often used in
visual tasks today. We propose a novel highly sparse linear hashing method
based on pairwise rotations. The encoding cost of the proposed algorithm is
$\mathrm{O}(n \log n)$ for n-dimensional features, whereas that of the existing
state-of-the-art method is typically $\mathrm{O}(n^2)$. The proposed method is
also remarkably faster in the learning phase. Along with the efficiency, the
retrieval accuracy is comparable to or slightly outperforming the
state-of-the-art. Pairwise rotations used in our method are formulated from an
analytical study of the trade-off relationship between quantization error and
entropy of binary codes. Although these hashing criteria are widely used in
previous researches, its analytical behavior is rarely studied. All building
blocks of our algorithm are based on the analytical solution, and it thus
provides a fairly simple and efficient procedure.
