{"id":"https://openalex.org/W2136554497","doi":"https://doi.org/10.1137/110825327","title":"Candecomp/Parafac: From Diverging Components to a Decomposition in Block Terms","display_name":"Candecomp/Parafac: From Diverging Components to a Decomposition in Block Terms","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2136554497","doi":"https://doi.org/10.1137/110825327","mag":"2136554497"},"language":"en","primary_location":{"id":"doi:10.1137/110825327","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110825327","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://pure.rug.nl/ws/files/66720325/110825327.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084820167","display_name":"Alwin Stegeman","orcid":"https://orcid.org/0000-0003-3385-2560"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Alwin Stegeman","raw_affiliation_strings":["Psychometrics and Statistics"],"affiliations":[{"raw_affiliation_string":"Psychometrics and Statistics","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5084820167"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.6215,"has_fulltext":true,"cited_by_count":31,"citation_normalized_percentile":{"value":0.87804878,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"33","issue":"2","first_page":"291","last_page":"316"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9998999834060669,"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":0.9998999834060669,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.978600025177002,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9700000286102295,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/mathematics","display_name":"Mathematics","score":0.7729028463363647},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.7035088539123535},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6858516335487366},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.5858672261238098},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.557415246963501},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5016474723815918},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.4923766851425171},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4769669771194458},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.471365362405777},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4299171268939972},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.4257392883300781},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.422794371843338},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.41098251938819885},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3009556233882904},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.26034942269325256},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16065311431884766},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.10071027278900146},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08221566677093506}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7729028463363647},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.7035088539123535},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6858516335487366},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.5858672261238098},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.557415246963501},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5016474723815918},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.4923766851425171},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4769669771194458},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.471365362405777},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4299171268939972},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.4257392883300781},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.422794371843338},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.41098251938819885},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3009556233882904},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.26034942269325256},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16065311431884766},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.10071027278900146},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08221566677093506},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/110825327","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110825327","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:pure.rug.nl:publications/0ab0fe27-60c9-4058-b784-973a192bc578","is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/0ab0fe27-60c9-4058-b784-973a192bc578","pdf_url":"https://pure.rug.nl/ws/files/66720325/110825327.pdf","source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Stegeman, A 2012, 'Candecomp/Parafac : From diverging components to a decomposition in block terms.', SIAM Journal on Matrix Analysis and Applications, vol. 33, no. 2, pp. 291-316. https://doi.org/10.1137/110825327","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:pure.rug.nl:publications/0ab0fe27-60c9-4058-b784-973a192bc578","is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/0ab0fe27-60c9-4058-b784-973a192bc578","pdf_url":"https://pure.rug.nl/ws/files/66720325/110825327.pdf","source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Stegeman, A 2012, 'Candecomp/Parafac : From diverging components to a decomposition in block terms.', SIAM Journal on Matrix Analysis and Applications, vol. 33, no. 2, pp. 291-316. https://doi.org/10.1137/110825327","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G629491556","display_name":null,"funder_award_id":"(NWO)","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2136554497.pdf","grobid_xml":"https://content.openalex.org/works/W2136554497.grobid-xml"},"referenced_works_count":55,"referenced_works":["https://openalex.org/W3392783","https://openalex.org/W158789882","https://openalex.org/W1963526037","https://openalex.org/W1963826206","https://openalex.org/W1965965675","https://openalex.org/W1986678274","https://openalex.org/W1989881099","https://openalex.org/W1992223193","https://openalex.org/W1996440503","https://openalex.org/W2000045479","https://openalex.org/W2000215628","https://openalex.org/W2008560788","https://openalex.org/W2009235538","https://openalex.org/W2011179711","https://openalex.org/W2019603005","https://openalex.org/W2021958990","https://openalex.org/W2023724794","https://openalex.org/W2024165284","https://openalex.org/W2024166170","https://openalex.org/W2025603201","https://openalex.org/W2026698804","https://openalex.org/W2035062691","https://openalex.org/W2047680880","https://openalex.org/W2048050794","https://openalex.org/W2050770124","https://openalex.org/W2057503509","https://openalex.org/W2057654102","https://openalex.org/W2073469810","https://openalex.org/W2075427932","https://openalex.org/W2076603483","https://openalex.org/W2078789945","https://openalex.org/W2082658029","https://openalex.org/W2092978222","https://openalex.org/W2096248848","https://openalex.org/W2097508397","https://openalex.org/W2099741732","https://openalex.org/W2101113459","https://openalex.org/W2101641981","https://openalex.org/W2105186495","https://openalex.org/W2112451877","https://openalex.org/W2112702842","https://openalex.org/W2121739212","https://openalex.org/W2132220618","https://openalex.org/W2132267493","https://openalex.org/W2136023375","https://openalex.org/W2140862024","https://openalex.org/W2149957412","https://openalex.org/W2150059498","https://openalex.org/W2156982859","https://openalex.org/W2162440838","https://openalex.org/W2170668800","https://openalex.org/W2172195418","https://openalex.org/W2258054274","https://openalex.org/W2330159389","https://openalex.org/W2915098601"],"related_works":["https://openalex.org/W2781510240","https://openalex.org/W2950186459","https://openalex.org/W2170114491","https://openalex.org/W2897298721","https://openalex.org/W2242624680","https://openalex.org/W2136127937","https://openalex.org/W4290987221","https://openalex.org/W2216309014","https://openalex.org/W2365701604","https://openalex.org/W3199841771"],"abstract_inverted_index":{"Fitting":[0],"an":[1,67,150],"R-component":[2],"Candecomp/Parafac":[3],"(CP)":[4],"decomposition":[5,86,99,162],"to":[6,17,35,56,69,108,155],"a":[7,19,27,84,98,109],"multiway":[8,42],"array":[9],"or":[10,127],"higher-order":[11],"tensor":[12],"${\\cal":[13,24,134,156],"Z}$":[14],"is":[15,49],"equivalent":[16],"finding":[18],"best":[20,28],"rank-R":[21,29],"approximation":[22,30,59],"of":[23,41,111,125,139,142,163,177],"Z}$.":[25],"Such":[26],"may":[31],"not":[32,50],"exist":[33],"due":[34],"the":[36,39,58,119,130,137,140,159],"fact":[37],"that":[38,83,117],"set":[40],"arrays":[43,78],"with":[44,79],"rank":[45],"at":[46],"most":[47],"R":[48],"closed.":[51],"In":[52],"this":[53],"case,":[54],"trying":[55],"compute":[57],"results":[60,172],"in":[61,100,123],"diverging":[62,71,92,112,120],"CP":[63,85,143],"components.":[64,113],"We":[65,81],"present":[66],"approach":[68],"avoid":[70],"components":[72,93,121],"for":[73],"real":[74],"$I\\times":[75],"J\\times":[76],"K$":[77],"$R\\le\\min(I,J,K)$.":[80],"show":[82,116],"$({\\bf":[87,164],"A},{\\bf":[88,165],"B},{\\bf":[89,166],"C})$":[90,167],"featuring":[91],"can":[94,145],"be":[95,146],"rewritten":[96],"as":[97,168],"block":[101,105,160],"terms,":[102],"where":[103],"each":[104],"term":[106,161],"corresponds":[107],"group":[110],"Moreover,":[114],"we":[115],"if":[118],"occur":[122],"groups":[124],"two":[126],"three,":[128],"then":[129],"limiting":[131],"boundary":[132],"point":[133],"X}$":[135],"(i.e.,":[136],"limit":[138],"sequence":[141],"updates)":[144],"obtained":[147],"by":[148,175],"fitting":[149],"appropriate":[151],"constrained":[152],"Tucker3":[153],"model":[154],"Z}$,":[157],"using":[158],"initial":[169],"values.":[170],"Our":[171],"are":[173],"demonstrated":[174],"means":[176],"numerical":[178],"experiments.":[179]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}