Fast Cross-polytope Locality-sensitive Hashing
Christopher Kennedy, Rachel Ward . Arxiv 2016 – 7 citations
[Paper]
We provide a variant of cross-polytope locality sensitive hashing with respect to angular distance which is provably optimal in asymptotic sensitivity and enjoys (\mathcal{O}(d \ln d )) hash computation time. Building on a recent result (by Andoni, Indyk, Laarhoven, Razenshteyn, Schmidt, 2015), we show that optimal asymptotic sensitivity for cross-polytope LSH is retained even when the dense Gaussian matrix is replaced by a fast Johnson-Lindenstrauss transform followed by discrete pseudo-rotation, reducing the hash computation time from (\mathcal{O}(d^2)) to (\mathcal{O}(d \ln d )). Moreover, our scheme achieves the optimal rate of convergence for sensitivity. By incorporating a low-randomness Johnson-Lindenstrauss transform, our scheme can be modified to require only (\mathcal{O}(\ln^9(d))) random bits