{"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-hash-functions-for-similarity","title":"Practical Hash Functions for Similarity Estimation and Dimensionality Reduction","arxiv_id":"1711.08797","date":"2017-11-23","proceeding":"NeurIPS 2017 12","authors":["Søren Dahlgaard","Mathias Bæk Tejs Knudsen","Mikkel Thorup"],"abstract":"Hashing is a basic tool for dimensionality reduction employed in several\naspects of machine learning. However, the perfomance analysis is often carried\nout under the abstract assumption that a truly random unit cost hash function\nis used, without concern for which concrete hash function is employed. The\nconcrete hash function may work fine on sufficiently random input. The question\nis if it can be trusted in the real world when faced with more structured\ninput.\n  In this paper we focus on two prominent applications of hashing, namely\nsimilarity estimation with the one permutation hashing (OPH) scheme of Li et\nal. [NIPS'12] and feature hashing (FH) of Weinberger et al. [ICML'09], both of\nwhich have found numerous applications, i.e. in approximate near-neighbour\nsearch with LSH and large-scale classification with SVM.\n  We consider mixed tabulation hashing of Dahlgaard et al.[FOCS'15] which was\nproved to perform like a truly random hash function in many applications,\nincluding OPH. Here we first show improved concentration bounds for FH with\ntruly random hashing and then argue that mixed tabulation performs similar for\nsparse input. Our main contribution, however, is an experimental comparison of\ndifferent hashing schemes when used inside FH, OPH, and LSH.\n  We find that mixed tabulation hashing is almost as fast as the\nmultiply-mod-prime scheme ax+b mod p. Mutiply-mod-prime is guaranteed to work\nwell on sufficiently random data, but we demonstrate that in the above\napplications, it can lead to bias and poor concentration on both real-world and\nsynthetic data. We also compare with the popular MurmurHash3, which has no\nproven guarantees. Mixed tabulation and MurmurHash3 both perform similar to\ntruly random hashing in our experiments. However, mixed tabulation is 40%\nfaster than MurmurHash3, and it has the proven guarantee of good performance on\nall possible input.","url_abs":"http://arxiv.org/abs/1711.08797v1","url_pdf":"http://arxiv.org/pdf/1711.08797v1.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-hash-functions-for-similarity","repo_url":"https://github.com/zera/Nips_MT","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"}],"methods":[{"method_slug":"svm","method_name":"SVM"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1711.08797","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}