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oai:drops-oai.dagstuhl.de:8193 2024-03-06T10:39:22Z ddc:004 open_access

Fast Cross-Polytope Locality-Sensitive Hashing Kennedy, Christopher Ward, Rachel Locality-sensitive hashing Dimension reduction Johnson-Lindenstrauss lemma 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 in (Andoni, Indyk, Laarhoven, Razenshteyn '15), 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Christopher Kennedy and Rachel Ward 2017 Is Part Of LIPIcs, Volume 67, 8th Innovations in Theoretical Computer Science Conference (ITCS 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ITCS.2017.53 urn:nbn:de:0030-drops-81936 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.53 eng https://creativecommons.org/licenses/by/3.0/legalcode