{"id":"https://openalex.org/W4242200182","doi":"https://doi.org/10.1137/140956865","title":"Coupled Canonical Polyadic Decompositions and (Coupled) Decompositions in Multilinear Rank- $(L_{r,n},L_{r,n},1)$ Terms---Part II: Algorithms","display_name":"Coupled Canonical Polyadic Decompositions and (Coupled) Decompositions in Multilinear Rank- $(L_{r,n},L_{r,n},1)$ Terms---Part II: Algorithms","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W4242200182","doi":"https://doi.org/10.1137/140956865"},"language":"en","primary_location":{"id":"doi:10.1137/140956865","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140956865","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://lirias.kuleuven.be/handle/123456789/463244","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079087496","display_name":"Mikael S\u00f8rensen","orcid":"https://orcid.org/0000-0003-4337-7417"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Mikael S\u00f8rensen","raw_affiliation_strings":["Group Science, Engineering and Technology, KU Leuven -Kulak, 8500 Kortrijk, Belgium, and"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Group Science, Engineering and Technology, KU Leuven -Kulak, 8500 Kortrijk, Belgium, and","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021106574","display_name":"Ignat Domanov","orcid":"https://orcid.org/0000-0001-7605-4177"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Ignat Domanov","raw_affiliation_strings":["Group Science, Engineering and Technology, KU Leuven -Kulak, 8500 Kortrijk, Belgium, and"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Group Science, Engineering and Technology, KU Leuven -Kulak, 8500 Kortrijk, Belgium, and","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009006026","display_name":"Lieven De Lathauwer","orcid":"https://orcid.org/0000-0001-5562-5014"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Lieven De Lathauwer","raw_affiliation_strings":["Group Science, Engineering and Technology, KU Leuven -Kulak, 8500 Kortrijk, Belgium, and"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Group Science, Engineering and Technology, KU Leuven -Kulak, 8500 Kortrijk, Belgium, and","institution_ids":["https://openalex.org/I99464096"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I99464096"],"apc_list":null,"apc_paid":null,"fwci":2.4641,"has_fulltext":false,"cited_by_count":69,"citation_normalized_percentile":{"value":0.89847716,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"36","issue":"3","first_page":"1015","last_page":"1045"},"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/T11447","display_name":"Blind Source Separation Techniques","score":0.998199999332428,"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9923999905586243,"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/multilinear-map","display_name":"Multilinear map","score":0.8901546597480774},{"id":"https://openalex.org/keywords/multilinear-algebra","display_name":"Multilinear algebra","score":0.8827885389328003},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7269311547279358},{"id":"https://openalex.org/keywords/linear-algebra","display_name":"Linear algebra","score":0.6815223097801208},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6543474793434143},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.599761962890625},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4517948627471924},{"id":"https://openalex.org/keywords/qr-decomposition","display_name":"QR decomposition","score":0.4295251965522766},{"id":"https://openalex.org/keywords/numerical-linear-algebra","display_name":"Numerical linear algebra","score":0.42172926664352417},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.4106990396976471},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.3667469918727875},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.23263666033744812},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.21707290410995483},{"id":"https://openalex.org/keywords/algebra-representation","display_name":"Algebra representation","score":0.1605066955089569},{"id":"https://openalex.org/keywords/jordan-algebra","display_name":"Jordan algebra","score":0.0900954008102417},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07909137010574341},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07707729935646057}],"concepts":[{"id":"https://openalex.org/C84392682","wikidata":"https://www.wikidata.org/wiki/Q1952404","display_name":"Multilinear map","level":2,"score":0.8901546597480774},{"id":"https://openalex.org/C60321788","wikidata":"https://www.wikidata.org/wiki/Q1197190","display_name":"Multilinear algebra","level":5,"score":0.8827885389328003},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7269311547279358},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.6815223097801208},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6543474793434143},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.599761962890625},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4517948627471924},{"id":"https://openalex.org/C188060507","wikidata":"https://www.wikidata.org/wiki/Q653242","display_name":"QR decomposition","level":3,"score":0.4295251965522766},{"id":"https://openalex.org/C163834973","wikidata":"https://www.wikidata.org/wiki/Q2004891","display_name":"Numerical linear algebra","level":3,"score":0.42172926664352417},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.4106990396976471},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3667469918727875},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.23263666033744812},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.21707290410995483},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.1605066955089569},{"id":"https://openalex.org/C100376341","wikidata":"https://www.wikidata.org/wiki/Q649977","display_name":"Jordan algebra","level":4,"score":0.0900954008102417},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07909137010574341},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07707729935646057},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/140956865","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140956865","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:lirias2repo.kuleuven.be:123456789/463244","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/463244","pdf_url":null,"source":{"id":"https://openalex.org/S7407055369","display_name":"Lirias","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"SIAM Journal on Matrix Analysis and Applications, vol. 36 (3), Art.No. 3, (1015-1045)","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/463244","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/463244","pdf_url":null,"source":{"id":"https://openalex.org/S7407055369","display_name":"Lirias","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"SIAM Journal on Matrix Analysis and Applications, vol. 36 (3), Art.No. 3, (1015-1045)","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W49160414","https://openalex.org/W1562564874","https://openalex.org/W1963826206","https://openalex.org/W1964650132","https://openalex.org/W1972547249","https://openalex.org/W1974785908","https://openalex.org/W1989811026","https://openalex.org/W2000045479","https://openalex.org/W2017948584","https://openalex.org/W2018282388","https://openalex.org/W2024165284","https://openalex.org/W2024166170","https://openalex.org/W2024182011","https://openalex.org/W2025603201","https://openalex.org/W2027201767","https://openalex.org/W2033154334","https://openalex.org/W2047680880","https://openalex.org/W2076214866","https://openalex.org/W2117756735","https://openalex.org/W2119412403","https://openalex.org/W2167083368","https://openalex.org/W2915098601","https://openalex.org/W3102183770"],"related_works":["https://openalex.org/W4229551161","https://openalex.org/W2242909499","https://openalex.org/W2405717268","https://openalex.org/W2021525945","https://openalex.org/W2525655506","https://openalex.org/W1982615145","https://openalex.org/W2889328065","https://openalex.org/W4313191723","https://openalex.org/W3169240678","https://openalex.org/W351153932"],"abstract_inverted_index":{"The":[0],"coupled":[1,31,48,78],"canonical":[2],"polyadic":[3],"decomposition":[4],"(CPD)":[5],"is":[6],"an":[7,59],"emerging":[8],"tool":[9],"for":[10,30],"the":[11,53,64,73],"joint":[12],"analysis":[13],"of":[14,52],"multiple":[15],"data":[16],"sets":[17],"in":[18,80],"signal":[19],"processing":[20],"and":[21,77],"statistics.":[22],"Despite":[23],"their":[24],"importance,":[25],"linear":[26,89],"algebra":[27,90],"based":[28,91],"algorithms":[29,92],"CPDs":[32,68],"have":[33],"not":[34],"yet":[35],"been":[36],"developed.":[37],"In":[38],"this":[39],"paper,":[40],"we":[41,57],"first":[42],"explain":[43],"how":[44],"to":[45,75],"obtain":[46],"a":[47,98],"CPD":[49],"from":[50],"one":[51],"individual":[54],"CPDs.":[55],"Next,":[56],"present":[58],"algorithm":[60],"that":[61,88],"directly":[62],"takes":[63],"coupling":[65],"between":[66],"several":[67],"into":[69],"account.":[70],"We":[71],"extend":[72],"methods":[74],"single":[76],"decompositions":[79],"multilinear":[81],"rank-$(L_{{r,n}},L_{{r,n}},1)$":[82],"terms.":[83],"Finally,":[84],"numerical":[85],"experiments":[86],"demonstrate":[87],"can":[93],"provide":[94],"good":[95],"results":[96],"at":[97],"reasonable":[99],"computational":[100],"cost.":[101]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2022-05-12T00:00:00"}