Practical and optimal LSH for angular distance

Alexandr Andoni, Piotr Indyk, T.M.M. Laarhoven, Ilya Razenshteyn, Ludwig Schmidt

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review


We show the existence of a Locality-Sensitive Hashing (LSH) family for the angular distance that yields an approximate Near Neighbor Search algorithm with the asymptotically optimal running time exponent. Unlike earlier algorithms with this property (e.g., Spherical LSH (Andoni-Indyk-Nguyen-Razenshteyn 2014) (Andoni-Razenshteyn 2015)), our algorithm is also practical, improving upon the well-studied hyperplane LSH (Charikar 2002) in practice. We also introduce a multiprobe version of this algorithm and conduct an experimental evaluation on real and synthetic data sets.We complement the above positive results with a fine-grained lower bound for the quality of any LSH family for angular distance. Our lower bound implies that the above LSH family exhibits a trade-off between evaluation time and quality that is close to optimal for a natural class of LSH functions.
Original languageEnglish
Title of host publicationAdvances in Neural Information Processing Systems (NIPS, Montreal, Canada, December 7-10, 2015)
EditorsC. Cortes, N.D. Lawrence, D.D. Lee, M. Sugiyama, R. Garnett
Place of Publications.l.
PublisherCurran Associates
Number of pages9
Publication statusPublished - 7 Dec 2015
EventAdvances in Neural Information Processing Systems (NIPS 2015) - Montreal, Canada
Duration: 7 Dec 201510 Dec 2015

Publication series

NameAdvances in Neutral Information Processing Systems


ConferenceAdvances in Neural Information Processing Systems (NIPS 2015)
Abbreviated titleNIPS

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