{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/practical-and-optimal-lsh-for-angular","title":"Practical and Optimal LSH for Angular Distance","arxiv_id":"1509.02897","date":"2015-09-09","proceeding":"NeurIPS 2015 12","authors":["Alexandr Andoni","Piotr Indyk","Thijs Laarhoven","Ilya Razenshteyn","Ludwig Schmidt"],"abstract":"We show the existence of a Locality-Sensitive Hashing (LSH) family for the\nangular distance that yields an approximate Near Neighbor Search algorithm with\nthe asymptotically optimal running time exponent. Unlike earlier algorithms\nwith this property (e.g., Spherical LSH [Andoni, Indyk, Nguyen, Razenshteyn\n2014], [Andoni, Razenshteyn 2015]), our algorithm is also practical, improving\nupon the well-studied hyperplane LSH [Charikar, 2002] in practice. We also\nintroduce a multiprobe version of this algorithm, and conduct experimental\nevaluation on real and synthetic data sets.\n  We complement the above positive results with a fine-grained lower bound for\nthe quality of any LSH family for angular distance. Our lower bound implies\nthat the above LSH family exhibits a trade-off between evaluation time and\nquality that is close to optimal for a natural class of LSH functions.","url_abs":"http://arxiv.org/abs/1509.02897v1","url_pdf":"http://arxiv.org/pdf/1509.02897v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"practical-and-optimal-lsh-for-angular","repo_url":"https://github.com/FALCONN-LIB/FFHT","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"NOASSERTION"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1509.02897","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}