{"id":"https://openalex.org/W2115807064","doi":"https://doi.org/10.1145/1553374.1553459","title":"Efficient Euclidean projections in linear time","display_name":"Efficient Euclidean projections in linear time","publication_year":2009,"publication_date":"2009-06-14","ids":{"openalex":"https://openalex.org/W2115807064","doi":"https://doi.org/10.1145/1553374.1553459","mag":"2115807064"},"language":"en","primary_location":{"id":"doi:10.1145/1553374.1553459","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1553374.1553459","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 26th Annual International Conference on Machine Learning","raw_type":"proceedings-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/A5100361699","display_name":"Jun Liu","orcid":"https://orcid.org/0000-0001-8697-3089"},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jun Liu","raw_affiliation_strings":["Arizona State University, Tempe, AZ"],"affiliations":[{"raw_affiliation_string":"Arizona State University, Tempe, AZ","institution_ids":["https://openalex.org/I55732556"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010419481","display_name":"Jieping Ye","orcid":"https://orcid.org/0000-0001-8662-5818"},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jieping Ye","raw_affiliation_strings":["Arizona State University, Tempe, AZ"],"affiliations":[{"raw_affiliation_string":"Arizona State University, Tempe, AZ","institution_ids":["https://openalex.org/I55732556"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100361699"],"corresponding_institution_ids":["https://openalex.org/I55732556"],"apc_list":null,"apc_paid":null,"fwci":15.2728,"has_fulltext":false,"cited_by_count":160,"citation_normalized_percentile":{"value":0.99431352,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"657","last_page":"664"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10057","display_name":"Face and Expression Recognition","score":0.9776999950408936,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.6334465742111206},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.5582364201545715},{"id":"https://openalex.org/keywords/polyhedron","display_name":"Polyhedron","score":0.5504414439201355},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5164668560028076},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.5070395469665527},{"id":"https://openalex.org/keywords/bisection-method","display_name":"Bisection method","score":0.496376097202301},{"id":"https://openalex.org/keywords/ball","display_name":"Ball (mathematics)","score":0.49300095438957214},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4797440767288208},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.45154473185539246},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4490280747413635},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43544429540634155},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.43474486470222473},{"id":"https://openalex.org/keywords/euclidean-distance-matrix","display_name":"Euclidean distance matrix","score":0.4152512550354004},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.31595689058303833},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1616138219833374}],"concepts":[{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.6334465742111206},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.5582364201545715},{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.5504414439201355},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5164668560028076},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.5070395469665527},{"id":"https://openalex.org/C157544257","wikidata":"https://www.wikidata.org/wiki/Q866300","display_name":"Bisection method","level":2,"score":0.496376097202301},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.49300095438957214},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4797440767288208},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.45154473185539246},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4490280747413635},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43544429540634155},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43474486470222473},{"id":"https://openalex.org/C171558263","wikidata":"https://www.wikidata.org/wiki/Q5406122","display_name":"Euclidean distance matrix","level":3,"score":0.4152512550354004},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.31595689058303833},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1616138219833374},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/1553374.1553459","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1553374.1553459","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 26th Annual International Conference on Machine Learning","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.150.5886","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.150.5886","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.mcgill.ca/~icml2009/papers/123.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7681389578","display_name":null,"funder_award_id":"IIS-0612069IIS-0812551CCF-0811790","funder_id":"https://openalex.org/F4320337387","funder_display_name":"Division of Computing and Communication Foundations"},{"id":"https://openalex.org/G8681176052","display_name":null,"funder_award_id":"IIS-0612069IIS-0812551CCF-0811790","funder_id":"https://openalex.org/F4320337389","funder_display_name":"Division of Information and Intelligent Systems"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337387","display_name":"Division of Computing and Communication Foundations","ror":"https://ror.org/01mng8331"},{"id":"https://openalex.org/F4320337389","display_name":"Division of Information and Intelligent Systems","ror":"https://ror.org/053a2cp42"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W64096456","https://openalex.org/W1978259121","https://openalex.org/W2004915807","https://openalex.org/W2027197817","https://openalex.org/W2046941888","https://openalex.org/W2118075434","https://openalex.org/W2118353660","https://openalex.org/W2119667497","https://openalex.org/W2135046866","https://openalex.org/W2296319761","https://openalex.org/W2296616510","https://openalex.org/W2752885492","https://openalex.org/W2997311912","https://openalex.org/W3001495003","https://openalex.org/W3141595720","https://openalex.org/W3145128584","https://openalex.org/W4250589301","https://openalex.org/W4250955649","https://openalex.org/W4285719527","https://openalex.org/W6602561656","https://openalex.org/W7029321148","https://openalex.org/W7074184022"],"related_works":["https://openalex.org/W2008939113","https://openalex.org/W3037672488","https://openalex.org/W2105228010","https://openalex.org/W2318206461","https://openalex.org/W4298154183","https://openalex.org/W37157938","https://openalex.org/W2090152127","https://openalex.org/W1965169884","https://openalex.org/W1566402893","https://openalex.org/W2622600204"],"abstract_inverted_index":{"We":[0,88],"consider":[1],"the":[2,6,21,25,93,97,110,118,123],"problem":[3],"of":[4,9,12,56,92,96],"computing":[5,122],"Euclidean":[7,68],"projection":[8],"a":[10,16,52],"vector":[11],"length":[13],"n":[14],"onto":[15],"closed":[17],"convex":[18],"set":[19],"including":[20],"l1":[22],"ball":[23],"and":[24,100],"specialized":[26],"polyhedra":[27],"employed":[28],"in":[29,41,83],"(Shalev-Shwartz":[30],"&":[31],"Singer,":[32],"2006).":[33],"These":[34],"problems":[35,73],"have":[36,51],"played":[37],"building":[38],"block":[39],"roles":[40],"solving":[42],"several":[43],"l1-norm":[44],"based":[45],"sparse":[46],"learning":[47],"problems.":[48],"Existing":[49],"methods":[50],"worst-case":[53],"time":[54,85],"complexity":[55],"O(n":[57],"log":[58],"n).":[59],"In":[60],"this":[61],"paper,":[62],"we":[63],"propose":[64,101],"to":[65],"cast":[66],"both":[67],"projections":[69],"as":[70],"root":[71],"finding":[72],"associated":[74],"with":[75],"specific":[76],"auxiliary":[77,98],"functions,":[78,99],"which":[79],"can":[80],"be":[81],"solved":[82],"linear":[84],"via":[86],"bisection.":[87],"further":[89],"make":[90],"use":[91],"special":[94],"structure":[95],"an":[102],"improved":[103],"bisection":[104],"algorithm.":[105],"Empirical":[106],"studies":[107],"demonstrate":[108],"that":[109],"proposed":[111],"algorithms":[112],"are":[113],"much":[114],"more":[115],"efficient":[116],"than":[117],"competing":[119],"ones":[120],"for":[121],"projections.":[124]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":15},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":15},{"year":2014,"cited_by_count":17},{"year":2013,"cited_by_count":13},{"year":2012,"cited_by_count":18}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}