{"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/improved-densification-of-one-permutation","title":"Improved Densification of One Permutation Hashing","arxiv_id":"1406.4784","date":"2014-06-18","proceeding":null,"authors":["Anshumali Shrivastava","Ping Li"],"abstract":"The existing work on densification of one permutation hashing reduces the\nquery processing cost of the $(K,L)$-parameterized Locality Sensitive Hashing\n(LSH) algorithm with minwise hashing, from $O(dKL)$ to merely $O(d + KL)$,\nwhere $d$ is the number of nonzeros of the data vector, $K$ is the number of\nhashes in each hash table, and $L$ is the number of hash tables. While that is\na substantial improvement, our analysis reveals that the existing densification\nscheme is sub-optimal. In particular, there is no enough randomness in that\nprocedure, which affects its accuracy on very sparse datasets.\n  In this paper, we provide a new densification procedure which is provably\nbetter than the existing scheme. This improvement is more significant for very\nsparse datasets which are common over the web. The improved technique has the\nsame cost of $O(d + KL)$ for query processing, thereby making it strictly\npreferable over the existing procedure. Experimental evaluations on public\ndatasets, in the task of hashing based near neighbor search, support our\ntheoretical findings.","url_abs":"http://arxiv.org/abs/1406.4784v1","url_pdf":"http://arxiv.org/pdf/1406.4784v1.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":"improved-densification-of-one-permutation","repo_url":"https://github.com/bigmlcom/sketchy","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}