{"id":"https://openalex.org/W3110664783","doi":"https://doi.org/10.1080/10618600.2020.1856118","title":"Tensor Canonical Correlation Analysis With Convergence and Statistical Guarantees","display_name":"Tensor Canonical Correlation Analysis With Convergence and Statistical Guarantees","publication_year":2020,"publication_date":"2020-12-04","ids":{"openalex":"https://openalex.org/W3110664783","doi":"https://doi.org/10.1080/10618600.2020.1856118","mag":"3110664783"},"language":"en","primary_location":{"id":"doi:10.1080/10618600.2020.1856118","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10618600.2020.1856118","pdf_url":null,"source":{"id":"https://openalex.org/S76159266","display_name":"Journal of Computational and Graphical Statistics","issn_l":"1061-8600","issn":["1061-8600","1537-2715"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational and Graphical Statistics","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/A5017956223","display_name":"You-Lin Chen","orcid":"https://orcid.org/0000-0002-8315-2602"},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"You-Lin Chen","raw_affiliation_strings":["Department of Statistics, The University of Chicago, Chicago, IL;"],"raw_orcid":"https://orcid.org/0000-0002-8315-2602","affiliations":[{"raw_affiliation_string":"Department of Statistics, The University of Chicago, Chicago, IL;","institution_ids":["https://openalex.org/I40347166"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016868056","display_name":"Mladen Kolar","orcid":"https://orcid.org/0000-0001-7353-3404"},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mladen Kolar","raw_affiliation_strings":["The University of Chicago Booth School of Business, Chicago, IL"],"raw_orcid":"https://orcid.org/0000-0001-7353-3404","affiliations":[{"raw_affiliation_string":"The University of Chicago Booth School of Business, Chicago, IL","institution_ids":["https://openalex.org/I40347166"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033579806","display_name":"Ruey S. Tsay","orcid":"https://orcid.org/0000-0002-4949-4035"},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ruey S. Tsay","raw_affiliation_strings":["The University of Chicago Booth School of Business, Chicago, IL"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The University of Chicago Booth School of Business, Chicago, IL","institution_ids":["https://openalex.org/I40347166"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5017956223"],"corresponding_institution_ids":["https://openalex.org/I40347166"],"apc_list":null,"apc_paid":null,"fwci":0.4784,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.5542571,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"30","issue":"3","first_page":"728","last_page":"744"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.965399980545044,"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9621000289916992,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/canonical-correlation","display_name":"Canonical correlation","score":0.8038623332977295},{"id":"https://openalex.org/keywords/canonical-analysis","display_name":"Canonical analysis","score":0.5956273674964905},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5669073462486267},{"id":"https://openalex.org/keywords/correlation","display_name":"Correlation","score":0.5250872373580933},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5189675688743591},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.5060388445854187},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45232874155044556},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3849681615829468},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35893481969833374},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2980634272098541},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18481779098510742},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13383597135543823},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08583474159240723}],"concepts":[{"id":"https://openalex.org/C153874254","wikidata":"https://www.wikidata.org/wiki/Q115542","display_name":"Canonical correlation","level":2,"score":0.8038623332977295},{"id":"https://openalex.org/C75806538","wikidata":"https://www.wikidata.org/wiki/Q5033360","display_name":"Canonical analysis","level":2,"score":0.5956273674964905},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5669073462486267},{"id":"https://openalex.org/C117220453","wikidata":"https://www.wikidata.org/wiki/Q5172842","display_name":"Correlation","level":2,"score":0.5250872373580933},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5189675688743591},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5060388445854187},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45232874155044556},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3849681615829468},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35893481969833374},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2980634272098541},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18481779098510742},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13383597135543823},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08583474159240723},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10618600.2020.1856118","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10618600.2020.1856118","pdf_url":null,"source":{"id":"https://openalex.org/S76159266","display_name":"Journal of Computational and Graphical Statistics","issn_l":"1061-8600","issn":["1061-8600","1537-2715"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational and Graphical Statistics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.5799999833106995}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":82,"referenced_works":["https://openalex.org/W1541521713","https://openalex.org/W1672347394","https://openalex.org/W1815537186","https://openalex.org/W1830879458","https://openalex.org/W1863007351","https://openalex.org/W1922505179","https://openalex.org/W1939652453","https://openalex.org/W1968154520","https://openalex.org/W1993468393","https://openalex.org/W2013912476","https://openalex.org/W2018282388","https://openalex.org/W2024165284","https://openalex.org/W2025341678","https://openalex.org/W2028795211","https://openalex.org/W2030434042","https://openalex.org/W2039954784","https://openalex.org/W2060204507","https://openalex.org/W2077612096","https://openalex.org/W2077813311","https://openalex.org/W2085789144","https://openalex.org/W2086400086","https://openalex.org/W2093417350","https://openalex.org/W2100235303","https://openalex.org/W2102544846","https://openalex.org/W2103537693","https://openalex.org/W2111411921","https://openalex.org/W2116680824","https://openalex.org/W2125290066","https://openalex.org/W2133148918","https://openalex.org/W2136069388","https://openalex.org/W2138768526","https://openalex.org/W2144070955","https://openalex.org/W2150382423","https://openalex.org/W2156204103","https://openalex.org/W2168380057","https://openalex.org/W2191558661","https://openalex.org/W2265744594","https://openalex.org/W2269587443","https://openalex.org/W2294798173","https://openalex.org/W2300599574","https://openalex.org/W2499811908","https://openalex.org/W2528161559","https://openalex.org/W2555690212","https://openalex.org/W2559655401","https://openalex.org/W2560674852","https://openalex.org/W2567289819","https://openalex.org/W2592362369","https://openalex.org/W2604272474","https://openalex.org/W2605800822","https://openalex.org/W2608702473","https://openalex.org/W2612690371","https://openalex.org/W2612972698","https://openalex.org/W2615280755","https://openalex.org/W2734856542","https://openalex.org/W2766386494","https://openalex.org/W2767058779","https://openalex.org/W2805907244","https://openalex.org/W2806658157","https://openalex.org/W2883611102","https://openalex.org/W2884790294","https://openalex.org/W2913668833","https://openalex.org/W2914584698","https://openalex.org/W2932904810","https://openalex.org/W2950049721","https://openalex.org/W2962715947","https://openalex.org/W2962826994","https://openalex.org/W2963248893","https://openalex.org/W2963413336","https://openalex.org/W2963763664","https://openalex.org/W2964106442","https://openalex.org/W2964146881","https://openalex.org/W2964255370","https://openalex.org/W3098183379","https://openalex.org/W3100208521","https://openalex.org/W3101586347","https://openalex.org/W3103366357","https://openalex.org/W3129194741","https://openalex.org/W4205293427","https://openalex.org/W4247950230","https://openalex.org/W4299828299","https://openalex.org/W4385738287","https://openalex.org/W6733934499"],"related_works":["https://openalex.org/W2121524531","https://openalex.org/W1565185441","https://openalex.org/W302711736","https://openalex.org/W2174400750","https://openalex.org/W1968846550","https://openalex.org/W1991315556","https://openalex.org/W2367413540","https://openalex.org/W1970646221","https://openalex.org/W2389459357","https://openalex.org/W2354853260"],"abstract_inverted_index":{"In":[0,38],"many":[1],"applications,":[2,150],"such":[3],"as":[4],"classification":[5],"of":[6,12,22,26,47,136,179,214],"images":[7],"or":[8],"videos,":[9],"it":[10],"is":[11,95],"interest":[13],"to":[14,29,32,71,85,101,162],"develop":[15,153],"a":[16,59,76,113,125,187,221],"framework":[17,84],"for":[18,190,234],"tensor":[19,99,230],"data":[20,28,56,87,115,143,199],"instead":[21],"an":[23,53,155,171],"ad-hoc":[24],"way":[25],"transforming":[27],"vectors":[30],"due":[31],"the":[33,67,72,90,103,119,134,164,177,210,215,227],"computational":[34],"and":[35,44,74,88,129,146,185,203,212],"under-sampling":[36],"issues.":[37],"this":[39,83,235],"article,":[40],"we":[41,81,130,151],"study":[42],"convergence":[43,132],"statistical":[45],"properties":[46],"two-dimensional":[48],"canonical":[49,104,193],"correlation":[50],"analysis":[51],"under":[52],"assumption":[54,141],"that":[55,64],"come":[57],"from":[58],"probabilistic":[60],"model.":[61],"We":[62],"show":[63,209],"carefully":[65],"initialized":[66],"power":[68,92],"method":[69,107],"converges":[70],"optimum":[73,181],"provide":[75],"finite":[77],"sample":[78],"bound.":[79],"Then":[80],"extend":[82],"tensor-valued":[86],"propose":[89],"higher-order":[91],"method,":[93],"which":[94,159,175],"commonly":[96],"used":[97,110],"in":[98,112,182,207,226],"decomposition,":[100],"extract":[102],"directions.":[105],"Our":[106,218],"can":[108],"be":[109],"effectively":[111],"large-scale":[114],"setting":[116],"by":[117],"solving":[118],"inner":[120],"least":[121],"squares":[122],"problem":[123,178],"with":[124],"stochastic":[126,166],"gradient":[127,167],"descent,":[128],"justify":[131],"via":[133],"theory":[135],"Lojasiewicz\u2019s":[137],"inequalities":[138],"without":[139],"any":[140],"on":[142,197,229],"generating":[144],"process":[145],"initialization.":[147],"For":[148],"practical":[149],"further":[152],"(a)":[154],"inexact":[156],"updating":[157],"scheme":[158,174],"allows":[160],"us":[161],"use":[163],"state-of-the-art":[165],"descent":[168],"algorithm,":[169],"(b)":[170],"effective":[172],"initialization":[173],"alleviates":[176],"local":[180],"nonconvex":[183],"optimization,":[184],"(c)":[186],"deflation":[188],"procedure":[189],"extracting":[191],"several":[192],"components.":[194],"Empirical":[195],"analyses":[196],"challenging":[198],"including":[200],"gene":[201],"expression":[202],"air":[204],"pollution":[205],"indexes":[206],"Taiwan,":[208],"effectiveness":[211],"efficiency":[213],"proposed":[216],"methodology.":[217],"results":[219],"fill":[220],"missing,":[222],"but":[223],"crucial,":[224],"part":[225],"literature":[228],"data.":[231],"Supplementary":[232],"materials":[233],"article":[236],"are":[237],"available":[238],"online.":[239]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2025-10-10T00:00:00"}