{"id":"https://openalex.org/W2093813380","doi":"https://doi.org/10.1137/060673096","title":"The Fast Johnson\u2013Lindenstrauss Transform and Approximate Nearest Neighbors","display_name":"The Fast Johnson\u2013Lindenstrauss Transform and Approximate Nearest Neighbors","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2093813380","doi":"https://doi.org/10.1137/060673096","mag":"2093813380"},"language":"en","primary_location":{"id":"doi:10.1137/060673096","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060673096","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033770678","display_name":"Nir Ailon","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nir Ailon","raw_affiliation_strings":["nailon@gmail.com#TAB#"],"affiliations":[{"raw_affiliation_string":"nailon@gmail.com#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044565966","display_name":"Bernard Chazelle","orcid":"https://orcid.org/0000-0001-8542-0247"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bernard Chazelle","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5033770678"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":25.2179,"has_fulltext":false,"cited_by_count":493,"citation_normalized_percentile":{"value":0.9975085,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"39","issue":"1","first_page":"302","last_page":"322"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10627","display_name":"Advanced Image and Video Retrieval Techniques","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hypercube","display_name":"Hypercube","score":0.6425577402114868},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6053386926651001},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.5731075406074524},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.5415546894073486},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4942200481891632},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.464829683303833},{"id":"https://openalex.org/keywords/random-projection","display_name":"Random projection","score":0.46074238419532776},{"id":"https://openalex.org/keywords/distortion","display_name":"Distortion (music)","score":0.41062310338020325},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35397255420684814},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26842835545539856},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12887242436408997},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09931489825248718}],"concepts":[{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.6425577402114868},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6053386926651001},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.5731075406074524},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5415546894073486},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4942200481891632},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.464829683303833},{"id":"https://openalex.org/C2777036070","wikidata":"https://www.wikidata.org/wiki/Q18393452","display_name":"Random projection","level":2,"score":0.46074238419532776},{"id":"https://openalex.org/C126780896","wikidata":"https://www.wikidata.org/wiki/Q899871","display_name":"Distortion (music)","level":4,"score":0.41062310338020325},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35397255420684814},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26842835545539856},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12887242436408997},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09931489825248718},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C194257627","wikidata":"https://www.wikidata.org/wiki/Q211554","display_name":"Amplifier","level":3,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/060673096","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060673096","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.217.9581","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.217.9581","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.princeton.edu/~chazelle/pubs/FJLT-sicomp09.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W73389528","https://openalex.org/W1499673022","https://openalex.org/W1503827365","https://openalex.org/W1568119442","https://openalex.org/W1626023514","https://openalex.org/W1951534873","https://openalex.org/W1970319631","https://openalex.org/W1971238646","https://openalex.org/W1983067644","https://openalex.org/W1991486559","https://openalex.org/W1991977420","https://openalex.org/W1998512964","https://openalex.org/W2013472589","https://openalex.org/W2013570814","https://openalex.org/W2024409132","https://openalex.org/W2037757210","https://openalex.org/W2043804332","https://openalex.org/W2045390367","https://openalex.org/W2046056514","https://openalex.org/W2046170126","https://openalex.org/W2062539466","https://openalex.org/W2063392856","https://openalex.org/W2063544484","https://openalex.org/W2068871408","https://openalex.org/W2071866949","https://openalex.org/W2088101210","https://openalex.org/W2089497633","https://openalex.org/W2093480133","https://openalex.org/W2097921974","https://openalex.org/W2104232723","https://openalex.org/W2122929038","https://openalex.org/W2124659530","https://openalex.org/W2134146845","https://openalex.org/W2138309709","https://openalex.org/W2147717514","https://openalex.org/W2154472578","https://openalex.org/W2167816765","https://openalex.org/W2176446742","https://openalex.org/W2427881153","https://openalex.org/W2979473749","https://openalex.org/W2983923309","https://openalex.org/W3043924052","https://openalex.org/W3097609957","https://openalex.org/W3147249397","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2495029940","https://openalex.org/W195224515","https://openalex.org/W2007173733","https://openalex.org/W2087725382","https://openalex.org/W2392648935","https://openalex.org/W4322716869","https://openalex.org/W2143269753","https://openalex.org/W2279178133","https://openalex.org/W226105639","https://openalex.org/W2151713270"],"abstract_inverted_index":{"We":[0,56,91,101,120],"introduce":[1],"a":[2,39,44,103,123],"new":[3],"low-distortion":[4,54,85],"embedding":[5],"of":[6,38,65,95],"$\\ell_2^d$":[7],"into":[8],"$\\ell_p^{O(\\log":[9],"n)}$":[10],"($p=1,2$)":[11],"called":[12],"the":[13,36,62,66,93,118,129],"fast":[14],"Johnson\u2013Lindenstrauss":[15],"transform":[16],"(FJLT).":[17],"The":[18,73],"FJLT":[19,74],"is":[20,33],"faster":[21,104,124],"than":[22],"standard":[23],"random":[24,49],"projections":[25,50],"and":[26,89],"just":[27],"as":[28],"easy":[29],"to":[30,78],"implement.":[31],"It":[32],"based":[34,83],"upon":[35],"preconditioning":[37],"sparse":[40],"projection":[41],"matrix":[42],"with":[43],"randomized":[45],"Fourier":[46,67],"transform.":[47],"Sparse":[48],"are":[51],"unsuitable":[52],"for":[53,126],"embeddings.":[55],"overcome":[57],"this":[58],"handicap":[59],"by":[60,115],"exploiting":[61],"\u201cHeisenberg":[63],"principle\u201d":[64],"transform,":[68],"i.e.,":[69],"its":[70],"local-global":[71],"duality.":[72],"can":[75],"be":[76],"used":[77],"speed":[79,112],"up":[80,113],"search":[81],"algorithms":[82],"on":[84],"embeddings":[86],"in":[87,99,117],"$\\ell_1$":[88],"$\\ell_2$.":[90],"consider":[92],"case":[94],"approximate":[96],"nearest":[97],"neighbors":[98],"$\\ell_2^d$.":[100],"provide":[102],"algorithm":[105,125],"using":[106],"classical":[107],"projections,":[108],"which":[109],"we":[110],"then":[111],"further":[114],"plugging":[116],"FJLT.":[119],"also":[121],"give":[122],"searching":[127],"over":[128],"hypercube.":[130]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":13},{"year":2024,"cited_by_count":25},{"year":2023,"cited_by_count":18},{"year":2022,"cited_by_count":24},{"year":2021,"cited_by_count":44},{"year":2020,"cited_by_count":43},{"year":2019,"cited_by_count":33},{"year":2018,"cited_by_count":38},{"year":2017,"cited_by_count":38},{"year":2016,"cited_by_count":38},{"year":2015,"cited_by_count":32},{"year":2014,"cited_by_count":29},{"year":2013,"cited_by_count":29},{"year":2012,"cited_by_count":16}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
