{"id":"https://openalex.org/W2009235538","doi":"https://doi.org/10.1137/080743354","title":"Uniqueness Conditions for Constrained Three-Way Factor Decompositions with Linearly Dependent Loadings","display_name":"Uniqueness Conditions for Constrained Three-Way Factor Decompositions with Linearly Dependent Loadings","publication_year":2009,"publication_date":"2009-12-23","ids":{"openalex":"https://openalex.org/W2009235538","doi":"https://doi.org/10.1137/080743354","mag":"2009235538"},"language":"en","primary_location":{"id":"doi:10.1137/080743354","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080743354","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://research.rug.nl/en/publications/0c5e6ff9-c1dd-4829-84a7-42f00b2f0b40","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":["a.w.stegeman@rug.nl#TAB#"],"affiliations":[{"raw_affiliation_string":"a.w.stegeman@rug.nl#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051813339","display_name":"Andr\u00e9 L. F. de Almeida","orcid":"https://orcid.org/0000-0002-3149-6307"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andr\u00e9 L. F. de Almeida","raw_affiliation_strings":["lima@i3s.unice.fr#TAB#"],"affiliations":[{"raw_affiliation_string":"lima@i3s.unice.fr#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5084820167"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.968,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.78280543,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"31","issue":"3","first_page":"1469","last_page":"1490"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9943000078201294,"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":0.9943000078201294,"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/T10575","display_name":"Wireless Communication Networks Research","score":0.9621000289916992,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9487000107765198,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.9297215938568115},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.866877555847168},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6544512510299683},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.5692763328552246},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5594884157180786},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5041159391403198},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.4626385271549225},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43999195098876953},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.40591275691986084},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3755040764808655},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2847670912742615},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12905189394950867}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.9297215938568115},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.866877555847168},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6544512510299683},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.5692763328552246},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5594884157180786},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5041159391403198},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4626385271549225},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43999195098876953},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40591275691986084},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3755040764808655},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2847670912742615},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12905189394950867},{"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":4,"locations":[{"id":"doi:10.1137/080743354","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080743354","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:openaire/0c5e6ff9-c1dd-4829-84a7-42f00b2f0b40","is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/0c5e6ff9-c1dd-4829-84a7-42f00b2f0b40","pdf_url":null,"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Stegeman, A & De Almeida, A L F 2009, 'Uniqueness conditions for constrained three-way factor decompositions with linearly dependent loadings', SIAM Journal on Matrix Analysis and Applications, vol. 31, no. 3, pp. 1469-1490. https://doi.org/10.1137/080743354","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:www.repositorio.ufc.br:riufc/779","is_oa":true,"landing_page_url":"http://www.repositorio.ufc.br/handle/riufc/779","pdf_url":"http://www.repositorio.ufc.br/handle/riufc/779","source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"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":"reponame:Reposit\u00f3rio Institucional da Universidade Federal do Cear\u00e1 (UFC)","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:pure.rug.nl:openaire_cris_publications/0c5e6ff9-c1dd-4829-84a7-42f00b2f0b40","is_oa":true,"landing_page_url":"https://hdl.handle.net/11370/0c5e6ff9-c1dd-4829-84a7-42f00b2f0b40","pdf_url":null,"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 & De Almeida, A L F 2009, 'Uniqueness conditions for constrained three-way factor decompositions with linearly dependent loadings', SIAM Journal on Matrix Analysis and Applications, vol. 31, no. 3, pp. 1469-1490. https://doi.org/10.1137/080743354","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:pure.rug.nl:openaire/0c5e6ff9-c1dd-4829-84a7-42f00b2f0b40","is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/0c5e6ff9-c1dd-4829-84a7-42f00b2f0b40","pdf_url":null,"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Stegeman, A & De Almeida, A L F 2009, 'Uniqueness conditions for constrained three-way factor decompositions with linearly dependent loadings', SIAM Journal on Matrix Analysis and Applications, vol. 31, no. 3, pp. 1469-1490. https://doi.org/10.1137/080743354","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[{"display_name":"Decent work and economic growth","id":"https://metadata.un.org/sdg/8","score":0.4099999964237213}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W227277429","https://openalex.org/W1548802052","https://openalex.org/W1963826206","https://openalex.org/W1989881099","https://openalex.org/W1998124716","https://openalex.org/W2000045479","https://openalex.org/W2000215628","https://openalex.org/W2008560788","https://openalex.org/W2010009888","https://openalex.org/W2013835207","https://openalex.org/W2019433413","https://openalex.org/W2024166170","https://openalex.org/W2027559251","https://openalex.org/W2029495869","https://openalex.org/W2033393326","https://openalex.org/W2035062691","https://openalex.org/W2047680880","https://openalex.org/W2050770124","https://openalex.org/W2051528376","https://openalex.org/W2057503509","https://openalex.org/W2076603483","https://openalex.org/W2078291856","https://openalex.org/W2082658029","https://openalex.org/W2099228589","https://openalex.org/W2099741732","https://openalex.org/W2101641981","https://openalex.org/W2101815756","https://openalex.org/W2111584844","https://openalex.org/W2112451877","https://openalex.org/W2112702842","https://openalex.org/W2119741678","https://openalex.org/W2121739212","https://openalex.org/W2131746221","https://openalex.org/W2132220618","https://openalex.org/W2132267493","https://openalex.org/W2136023375","https://openalex.org/W2156982859","https://openalex.org/W2158071874","https://openalex.org/W2160941078","https://openalex.org/W2162440838","https://openalex.org/W2163519125","https://openalex.org/W2170668800","https://openalex.org/W2258054274","https://openalex.org/W2330159389","https://openalex.org/W2915098601"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W4301247218","https://openalex.org/W2129818458","https://openalex.org/W4243074410","https://openalex.org/W4289551052","https://openalex.org/W4390756076","https://openalex.org/W2365701604"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"derive":[4],"uniqueness":[5,113,117,128],"conditions":[6,114,118],"for":[7,119],"a":[8,26,30,53,81],"constrained":[9,130],"version":[10],"of":[11,33,63,129,146],"the":[12,44,60,73,92,98,104,125,134],"parallel":[13],"factor":[14],"(Parafac)":[15],"decomposition,":[16],"also":[17],"known":[18,58,86],"as":[19,59,87],"canonical":[20],"decomposition":[21,105,136],"(Candecomp).":[22],"Candecomp/Parafac":[23],"(CP)":[24],"decomposes":[25],"three-way":[27,99],"array":[28],"into":[29],"prespecified":[31,54,82],"number":[32],"outer":[34,45,74],"product":[35,46,75],"arrays.":[36],"The":[37],"constraint":[38],"is":[39,57,68],"that":[40],"some":[41,70],"vectors":[42,71],"forming":[43,72],"arrays":[47,76],"are":[48,77,85,142],"linearly":[49],"dependent":[50],"according":[51,79],"to":[52,80],"pattern.":[55,83],"This":[56],"PARALIND":[61,120],"family":[62],"models.":[64],"An":[65],"important":[66],"subclass":[67],"where":[69],"repeated":[78],"These":[84],"CONFAC":[88,122],"decompositions.":[89],"We":[90,109],"discuss":[91,124],"relation":[93,126],"between":[94],"PARALIND,":[95],"CONFAC,":[96],"and":[97,103,115,121,123,133],"decompositions":[100],"CP,":[101],"Tucker3,":[102],"in":[106,137],"block":[107,135],"terms.":[108,139],"provide":[110],"both":[111],"essential":[112],"partial":[116],"with":[127],"Tucker3":[131],"models":[132],"rank-$(L,L,1)$":[138],"Our":[140],"results":[141],"demonstrated":[143],"by":[144],"means":[145],"examples.":[147]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":7}],"updated_date":"2026-03-28T08:17:26.163206","created_date":"2025-10-10T00:00:00"}