{"id":"https://openalex.org/W2743085632","doi":"https://doi.org/10.1162/neco_a_00996","title":"Constrained ERM Learning of Canonical Correlation Analysis: A Least Squares Perspective","display_name":"Constrained ERM Learning of Canonical Correlation Analysis: A Least Squares Perspective","publication_year":2017,"publication_date":"2017-08-04","ids":{"openalex":"https://openalex.org/W2743085632","doi":"https://doi.org/10.1162/neco_a_00996","mag":"2743085632","pmid":"https://pubmed.ncbi.nlm.nih.gov/28777729"},"language":"en","primary_location":{"id":"doi:10.1162/neco_a_00996","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco_a_00996","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","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/A5033196884","display_name":"Jia Cai","orcid":"https://orcid.org/0000-0001-8942-8668"},"institutions":[{"id":"https://openalex.org/I201459984","display_name":"Guangdong University Of Finances and Economics","ror":"https://ror.org/0459pv085","country_code":"CN","type":"education","lineage":["https://openalex.org/I201459984"]},{"id":"https://openalex.org/I4210149618","display_name":"Guangdong University of Finance","ror":"https://ror.org/04grzdh47","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210149618"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jia Cai","raw_affiliation_strings":["School of Mathematics and Statistics, Guangdong University of Finance and Economics, Guangzhou, Guangdong, 510320, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Guangdong University of Finance and Economics, Guangzhou, Guangdong, 510320, China","institution_ids":["https://openalex.org/I201459984","https://openalex.org/I4210149618"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029471997","display_name":"Hongwei Sun","orcid":null},"institutions":[{"id":"https://openalex.org/I34949971","display_name":"University of Jinan","ror":"https://ror.org/02mjz6f26","country_code":"CN","type":"education","lineage":["https://openalex.org/I34949971"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hongwei Sun","raw_affiliation_strings":["School of Science, University of Jinan, Jinan, Shandong, 250022, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, University of Jinan, Jinan, Shandong, 250022, China","institution_ids":["https://openalex.org/I34949971"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5029471997","https://openalex.org/A5033196884"],"corresponding_institution_ids":["https://openalex.org/I201459984","https://openalex.org/I34949971","https://openalex.org/I4210149618"],"apc_list":null,"apc_paid":null,"fwci":0.1848,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.5708073,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"29","issue":"10","first_page":"2825","last_page":"2859"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9997000098228455,"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/T10885","display_name":"Gene expression and cancer classification","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9898999929428101,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/canonical-correlation","display_name":"Canonical correlation","score":0.8797289729118347},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6039375066757202},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.5738064646720886},{"id":"https://openalex.org/keywords/dependency","display_name":"Dependency (UML)","score":0.5638344287872314},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5091027617454529},{"id":"https://openalex.org/keywords/latent-variable","display_name":"Latent variable","score":0.4894212782382965},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45881423354148865},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.43510156869888306},{"id":"https://openalex.org/keywords/perspective","display_name":"Perspective (graphical)","score":0.41939088702201843},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3852490782737732},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3725435733795166},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3435015380382538},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2598181366920471},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.12175121903419495}],"concepts":[{"id":"https://openalex.org/C153874254","wikidata":"https://www.wikidata.org/wiki/Q115542","display_name":"Canonical correlation","level":2,"score":0.8797289729118347},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6039375066757202},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.5738064646720886},{"id":"https://openalex.org/C19768560","wikidata":"https://www.wikidata.org/wiki/Q320727","display_name":"Dependency (UML)","level":2,"score":0.5638344287872314},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5091027617454529},{"id":"https://openalex.org/C51167844","wikidata":"https://www.wikidata.org/wiki/Q4422623","display_name":"Latent variable","level":2,"score":0.4894212782382965},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45881423354148865},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.43510156869888306},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.41939088702201843},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3852490782737732},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3725435733795166},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3435015380382538},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2598181366920471},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.12175121903419495}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1162/neco_a_00996","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco_a_00996","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},{"id":"pmid:28777729","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/28777729","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":"Neural computation","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322725","display_name":"China Scholarship Council","ror":"https://ror.org/04atp4p48"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":49,"referenced_works":["https://openalex.org/W114341944","https://openalex.org/W1210424432","https://openalex.org/W1497960466","https://openalex.org/W1523385540","https://openalex.org/W1536675765","https://openalex.org/W1664345024","https://openalex.org/W1972193544","https://openalex.org/W1972598934","https://openalex.org/W1975077471","https://openalex.org/W1976661283","https://openalex.org/W1988844573","https://openalex.org/W1992228381","https://openalex.org/W2000021956","https://openalex.org/W2001600470","https://openalex.org/W2025341678","https://openalex.org/W2047631354","https://openalex.org/W2048305372","https://openalex.org/W2076455317","https://openalex.org/W2085789144","https://openalex.org/W2089028133","https://openalex.org/W2098290597","https://openalex.org/W2100235303","https://openalex.org/W2108659514","https://openalex.org/W2112531253","https://openalex.org/W2123856749","https://openalex.org/W2125972593","https://openalex.org/W2130055251","https://openalex.org/W2145395365","https://openalex.org/W2155653793","https://openalex.org/W2156204103","https://openalex.org/W2158698691","https://openalex.org/W2257512704","https://openalex.org/W2279956800","https://openalex.org/W2337541833","https://openalex.org/W2595697910","https://openalex.org/W2606536620","https://openalex.org/W2913668833","https://openalex.org/W2917969515","https://openalex.org/W2949745249","https://openalex.org/W2949967295","https://openalex.org/W2950749759","https://openalex.org/W2999905431","https://openalex.org/W3102157992","https://openalex.org/W3126008680","https://openalex.org/W3144619878","https://openalex.org/W4245558064","https://openalex.org/W4285719527","https://openalex.org/W4289920060","https://openalex.org/W4299416517"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W63071447","https://openalex.org/W2888625260","https://openalex.org/W2354833674","https://openalex.org/W926365172","https://openalex.org/W2087395955","https://openalex.org/W4295111189","https://openalex.org/W2001059210","https://openalex.org/W2510815162","https://openalex.org/W2612756757"],"abstract_inverted_index":{"Canonical":[0],"correlation":[1],"analysis":[2,21],"(CCA)":[3],"is":[4,27,91,100],"a":[5,24,45,51,61],"useful":[6],"tool":[7],"in":[8,78],"detecting":[9],"the":[10,31,39,70,75,79,84,103,118,123],"latent":[11],"relationship":[12],"between":[13],"two":[14],"sets":[15,116],"of":[16,22,33,42,57,96,106,122],"multivariate":[17],"variables.":[18],"In":[19,69],"theoretical":[20,89],"CCA,":[23],"regularization":[25],"technique":[26],"utilized":[28],"to":[29,66,102],"investigate":[30],"consistency":[32,40,90,95],"its":[34],"analysis.":[35],"This":[36],"letter":[37],"addresses":[38],"property":[41],"CCA":[43,58],"from":[44],"least":[46],"squares":[47],"view.":[48],"We":[49],"construct":[50],"constrained":[52],"empirical":[53],"risk":[54],"minimization":[55],"framework":[56],"and":[59,77,113,120],"apply":[60],"two-stage":[62],"randomized":[63],"Kaczmarz":[64],"method":[65],"solve":[67],"it.":[68,107],"first":[71],"stage,":[72,81],"we":[73,82],"remove":[74],"noise,":[76],"second":[80],"compute":[83],"canonical":[85],"weight":[86],"vectors.":[87],"Rigorous":[88],"addressed.":[92],"The":[93],"statistical":[94],"this":[97],"novel":[98],"scenario":[99],"extended":[101],"kernel":[104],"version":[105],"Moreover,":[108],"experiments":[109],"on":[110],"both":[111],"synthetic":[112],"real-world":[114],"data":[115],"demonstrate":[117],"effectiveness":[119],"efficiency":[121],"proposed":[124],"algorithms.":[125]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}