Practical and optimal LSH for angular distance
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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.
Date issued
2015-12Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer ScienceJournal
Advances in Neural Information Processing Systems 28 (NIPS 2015)
Publisher
Neural Information Processing Systems Foundation
Citation
Andoni, Alexandr et al. "Practical and optimal LSH for angular distance." Advances in Neural Information Processing Systems 28 (NIPS 2015), 7-12 December, 2015, Montreal, Canada, Neural Information Processing Systems Foundation, 2015.
Version: Final published version