{"id":"https://openalex.org/W3045916244","doi":"https://doi.org/10.1109/tpami.2020.3012541","title":"A Self-Consistent-Field Iteration for Orthogonal Canonical Correlation Analysis","display_name":"A Self-Consistent-Field Iteration for Orthogonal Canonical Correlation Analysis","publication_year":2020,"publication_date":"2020-07-28","ids":{"openalex":"https://openalex.org/W3045916244","doi":"https://doi.org/10.1109/tpami.2020.3012541","mag":"3045916244","pmid":"https://pubmed.ncbi.nlm.nih.gov/32750837"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2020.3012541","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2020.3012541","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5102019567","display_name":"Lei\u2010Hong Zhang","orcid":"https://orcid.org/0000-0001-5349-8621"},"institutions":[{"id":"https://openalex.org/I181679659","display_name":"Shanghai University of Finance and Economics","ror":"https://ror.org/00wtvfq62","country_code":"CN","type":"education","lineage":["https://openalex.org/I181679659"]},{"id":"https://openalex.org/I3923682","display_name":"Soochow University","ror":"https://ror.org/05t8y2r12","country_code":"CN","type":"education","lineage":["https://openalex.org/I3923682"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lei-Hong Zhang","raw_affiliation_strings":["School of Mathematical Sciences and Institute of Computational Science, Soochow University, Suzhou, Jiangsu, China","School of Mathematics, Shanghai University of Finance and Economics, Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences and Institute of Computational Science, Soochow University, Suzhou, Jiangsu, China","institution_ids":["https://openalex.org/I3923682"]},{"raw_affiliation_string":"School of Mathematics, Shanghai University of Finance and Economics, Shanghai, China","institution_ids":["https://openalex.org/I181679659"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100336208","display_name":"Li Wang","orcid":"https://orcid.org/0000-0003-2658-4262"},"institutions":[{"id":"https://openalex.org/I189196454","display_name":"The University of Texas at Arlington","ror":"https://ror.org/019kgqr73","country_code":"US","type":"education","lineage":["https://openalex.org/I189196454"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Li Wang","raw_affiliation_strings":["Department of Mathematics and Department of Computer Science and Engineering, University of Texas at Arlington, Arlington, TX, USA"],"raw_orcid":"https://orcid.org/0000-0003-2658-4262","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Department of Computer Science and Engineering, University of Texas at Arlington, Arlington, TX, USA","institution_ids":["https://openalex.org/I189196454"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053733794","display_name":"Zhaojun Bai","orcid":"https://orcid.org/0000-0002-1143-2429"},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhaojun Bai","raw_affiliation_strings":["Department of Computer Science and Department of Mathematics, University of California, Davis, CA, USA"],"raw_orcid":"https://orcid.org/0000-0002-1143-2429","affiliations":[{"raw_affiliation_string":"Department of Computer Science and Department of Mathematics, University of California, Davis, CA, USA","institution_ids":["https://openalex.org/I84218800"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011252539","display_name":"Ren\u2010Cang Li","orcid":"https://orcid.org/0000-0002-4388-3398"},"institutions":[{"id":"https://openalex.org/I189196454","display_name":"The University of Texas at Arlington","ror":"https://ror.org/019kgqr73","country_code":"US","type":"education","lineage":["https://openalex.org/I189196454"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ren-Cang Li","raw_affiliation_strings":["Department of Mathematics, University of Texas at Arlington, Arlington, TX, USA"],"raw_orcid":"https://orcid.org/0000-0002-4388-3398","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Texas at Arlington, Arlington, TX, USA","institution_ids":["https://openalex.org/I189196454"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.977,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.86916254,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"44","issue":"2","first_page":"890","last_page":"904"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10640","display_name":"Spectroscopy and Chemometric Analyses","score":0.9815999865531921,"subfield":{"id":"https://openalex.org/subfields/1602","display_name":"Analytical Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.968999981880188,"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/karush\u2013kuhn\u2013tucker-conditions","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","score":0.7314693927764893},{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.5990440249443054},{"id":"https://openalex.org/keywords/trace","display_name":"TRACE (psycholinguistics)","score":0.5453729629516602},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.49988698959350586},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.47112414240837097},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46626386046409607},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4437854588031769},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4362500309944153},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.42777952551841736},{"id":"https://openalex.org/keywords/canonical-correlation","display_name":"Canonical correlation","score":0.41856762766838074},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3432161808013916},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.23763862252235413}],"concepts":[{"id":"https://openalex.org/C50454189","wikidata":"https://www.wikidata.org/wiki/Q2075125","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","level":2,"score":0.7314693927764893},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.5990440249443054},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.5453729629516602},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.49988698959350586},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.47112414240837097},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46626386046409607},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4437854588031769},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4362500309944153},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.42777952551841736},{"id":"https://openalex.org/C153874254","wikidata":"https://www.wikidata.org/wiki/Q115542","display_name":"Canonical correlation","level":2,"score":0.41856762766838074},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3432161808013916},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.23763862252235413},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","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:10.1109/tpami.2020.3012541","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2020.3012541","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},{"id":"pmid:32750837","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/32750837","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on pattern analysis and machine intelligence","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1318401113","display_name":null,"funder_award_id":"2018YFB0204404","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G1877213448","display_name":null,"funder_award_id":"DMS-1719620","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G1914270947","display_name":null,"funder_award_id":"DMS-1913364","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6066137772","display_name":null,"funder_award_id":"NSFC-11671246","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7583621034","display_name":null,"funder_award_id":"DMS-2009689","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W83404773","https://openalex.org/W1488435683","https://openalex.org/W1566135517","https://openalex.org/W1984983329","https://openalex.org/W2017530772","https://openalex.org/W2022286021","https://openalex.org/W2033478416","https://openalex.org/W2034517375","https://openalex.org/W2042141836","https://openalex.org/W2051142108","https://openalex.org/W2052684427","https://openalex.org/W2059586807","https://openalex.org/W2091127828","https://openalex.org/W2096663965","https://openalex.org/W2110662303","https://openalex.org/W2111427896","https://openalex.org/W2146241755","https://openalex.org/W2156935079","https://openalex.org/W2159184562","https://openalex.org/W2162915993","https://openalex.org/W2163352848","https://openalex.org/W2166049352","https://openalex.org/W2261652123","https://openalex.org/W2266012714","https://openalex.org/W2342748186","https://openalex.org/W2498996515","https://openalex.org/W2767589925","https://openalex.org/W2889240504","https://openalex.org/W2889864884","https://openalex.org/W2896604562","https://openalex.org/W3005272312","https://openalex.org/W3120740533","https://openalex.org/W4205293427","https://openalex.org/W4229666556","https://openalex.org/W4230094279","https://openalex.org/W4237723258","https://openalex.org/W4237951138","https://openalex.org/W4238885544","https://openalex.org/W4297817021","https://openalex.org/W4301491118","https://openalex.org/W4312258136","https://openalex.org/W6640795912","https://openalex.org/W6676974520","https://openalex.org/W6684134493","https://openalex.org/W6686785280","https://openalex.org/W6697129201","https://openalex.org/W6704120646","https://openalex.org/W6736484938"],"related_works":["https://openalex.org/W2155858901","https://openalex.org/W2491194410","https://openalex.org/W4382519099","https://openalex.org/W1515727993","https://openalex.org/W2037179686","https://openalex.org/W2802398440","https://openalex.org/W2085074295","https://openalex.org/W4236808165","https://openalex.org/W2732076076","https://openalex.org/W3011927635"],"abstract_inverted_index":{"We":[0,124],"propose":[1,72,137],"an":[2,73,88,138,142],"efficient":[3,61,139],"algorithm":[4,140],"for":[5,36,45,96,132],"solving":[6,46],"orthogonal":[7,19,133],"canonical":[8],"correlation":[9],"analysis":[10],"(OCCA)":[11],"in":[12,83],"the":[13,80,84,106,118,151,160,190],"form":[14,86],"of":[15,169],"trace-fractional":[16,85,129],"structure":[17],"and":[18,29,40,116,136,172],"linear":[20],"projections.":[21],"Even":[22],"though":[23],"orthogonality":[24,89],"has":[25],"been":[26],"widely":[27],"used":[28],"proved":[30,104],"to":[31,112,158,186],"be":[32],"a":[33,56,113,127],"useful":[34],"criterion":[35],"visualization,":[37],"pattern":[38],"recognition":[39],"feature":[41,174],"extraction,":[42],"existing":[43,164,191],"methods":[44,181,192],"OCCA":[47],"problem":[48,82,99,131],"are":[49,156,195],"either":[50,143],"numerically":[51],"unstable":[52],"by":[53,62],"relying":[54],"on":[55,150],"deflation":[57],"scheme,":[58],"or":[59,145,187],"less":[60],"directly":[63],"using":[64],"generic":[65],"optimization":[66],"methods.":[67],"In":[68],"this":[69,97],"paper,":[70],"we":[71],"alternating":[74,119],"numerical":[75,120],"scheme":[76,121,148],"whose":[77],"core":[78],"is":[79,100,103,109],"sub-maximization":[81,98],"with":[87,141],"constraint.":[90],"A":[91],"customized":[92],"self-consistent-field":[93],"(SCF)":[94],"iteration":[95,108],"devised.":[101],"It":[102],"that":[105,117,179],"SCF":[107,152],"globally":[110],"convergent":[111],"KKT":[114],"point":[115],"always":[122],"converges.":[123],"further":[125],"formulate":[126],"new":[128],"maximization":[130],"multiset":[134],"CCA":[135],"Jacobi-style":[144],"Gauss-Seidel-style":[146],"updating":[147],"based":[149],"iteration.":[153],"Extensive":[154],"experiments":[155],"conducted":[157],"evaluate":[159],"proposed":[161],"algorithms":[162],"against":[163],"methods,":[165],"including":[166],"real-world":[167],"applications":[168],"multi-label":[170],"classification":[171],"multi-view":[173],"extraction.":[175],"Experimental":[176],"results":[177],"show":[178],"our":[180],"not":[182],"only":[183],"perform":[184],"competitively":[185],"better":[188],"than":[189],"but":[193],"also":[194],"more":[196],"efficient.":[197]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":7},{"year":2020,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}