{"id":"https://openalex.org/W1963699590","doi":"https://doi.org/10.1137/100814615","title":"On Uniqueness of the Canonical Tensor Decomposition with Some Form of Symmetry","display_name":"On Uniqueness of the Canonical Tensor Decomposition with Some Form of Symmetry","publication_year":2011,"publication_date":"2011-04-01","ids":{"openalex":"https://openalex.org/W1963699590","doi":"https://doi.org/10.1137/100814615","mag":"1963699590"},"language":"en","primary_location":{"id":"doi:10.1137/100814615","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100814615","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/66721103/100814615.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":1.0448,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.73684211,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"32","issue":"2","first_page":"561","last_page":"583"},"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.955299973487854,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9459999799728394,"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/uniqueness","display_name":"Uniqueness","score":0.9611083269119263},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8871268033981323},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.7021727561950684},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.5689727663993835},{"id":"https://openalex.org/keywords/symmetric-tensor","display_name":"Symmetric tensor","score":0.5481774806976318},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5409276485443115},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.512183666229248},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.49446702003479004},{"id":"https://openalex.org/keywords/uniqueness-theorem-for-poissons-equation","display_name":"Uniqueness theorem for Poisson's equation","score":0.45207950472831726},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35221290588378906},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3346310555934906},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29480189085006714},{"id":"https://openalex.org/keywords/exact-solutions-in-general-relativity","display_name":"Exact solutions in general relativity","score":0.10959431529045105},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1011444628238678}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.9611083269119263},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8871268033981323},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.7021727561950684},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5689727663993835},{"id":"https://openalex.org/C20178491","wikidata":"https://www.wikidata.org/wiki/Q2204117","display_name":"Symmetric tensor","level":3,"score":0.5481774806976318},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5409276485443115},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.512183666229248},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.49446702003479004},{"id":"https://openalex.org/C155940","wikidata":"https://www.wikidata.org/wiki/Q7886967","display_name":"Uniqueness theorem for Poisson's equation","level":3,"score":0.45207950472831726},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35221290588378906},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3346310555934906},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29480189085006714},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.10959431529045105},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1011444628238678},{"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:10.1137/100814615","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100814615","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/fd0c14ff-1d42-44bf-a905-393d3a34f927","is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/fd0c14ff-1d42-44bf-a905-393d3a34f927","pdf_url":"https://pure.rug.nl/ws/files/66721103/100814615.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 2011, 'On uniqueness of the canonical tensor decomposition with some form of symmetry', SIAM Journal on Matrix Analysis and Applications, vol. 32, no. 2, pp. 561 - 583. https://doi.org/10.1137/100814615","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:pure.rug.nl:publications/fd0c14ff-1d42-44bf-a905-393d3a34f927","is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/fd0c14ff-1d42-44bf-a905-393d3a34f927","pdf_url":"https://pure.rug.nl/ws/files/66721103/100814615.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 2011, 'On uniqueness of the canonical tensor decomposition with some form of symmetry', SIAM Journal on Matrix Analysis and Applications, vol. 32, no. 2, pp. 561 - 583. https://doi.org/10.1137/100814615","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3462424673","display_name":null,"funder_award_id":"VIDI_grant","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"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":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W1963699590.pdf"},"referenced_works_count":50,"referenced_works":["https://openalex.org/W3392783","https://openalex.org/W227277429","https://openalex.org/W1548802052","https://openalex.org/W1963526037","https://openalex.org/W1986678274","https://openalex.org/W1992223193","https://openalex.org/W2000215628","https://openalex.org/W2008560788","https://openalex.org/W2010560128","https://openalex.org/W2024165284","https://openalex.org/W2024166170","https://openalex.org/W2027559251","https://openalex.org/W2029495869","https://openalex.org/W2035062691","https://openalex.org/W2037728586","https://openalex.org/W2047680880","https://openalex.org/W2050770124","https://openalex.org/W2057503509","https://openalex.org/W2064227455","https://openalex.org/W2076603483","https://openalex.org/W2078291856","https://openalex.org/W2082658029","https://openalex.org/W2097508397","https://openalex.org/W2099741732","https://openalex.org/W2101113459","https://openalex.org/W2101641981","https://openalex.org/W2102950139","https://openalex.org/W2108993730","https://openalex.org/W2112451877","https://openalex.org/W2112702842","https://openalex.org/W2121739212","https://openalex.org/W2124195644","https://openalex.org/W2125518871","https://openalex.org/W2132220618","https://openalex.org/W2132267493","https://openalex.org/W2136023375","https://openalex.org/W2136554497","https://openalex.org/W2138996475","https://openalex.org/W2139457438","https://openalex.org/W2140862024","https://openalex.org/W2142638745","https://openalex.org/W2150059498","https://openalex.org/W2156982859","https://openalex.org/W2158218920","https://openalex.org/W2163246442","https://openalex.org/W2170668800","https://openalex.org/W2225937484","https://openalex.org/W2258054274","https://openalex.org/W2330159389","https://openalex.org/W2915098601"],"related_works":["https://openalex.org/W3172166127","https://openalex.org/W4243074410","https://openalex.org/W2170114491","https://openalex.org/W2242624680","https://openalex.org/W2950186459","https://openalex.org/W2781510240","https://openalex.org/W2897298721","https://openalex.org/W2216309014","https://openalex.org/W2952474002","https://openalex.org/W4301967441"],"abstract_inverted_index":{"We":[0,97],"study":[1],"the":[2,5,26,78,81,84,95,99,118,144,150],"uniqueness":[3,43,62,72,114,129],"of":[4,7,19,29,83,94,104,134],"decomposition":[6,32,100],"an":[8],"th":[9],"order":[10],"tensor":[11],"(also":[12],"called":[13],"-way":[14],"array)":[15],"into":[16],"a":[17,41],"sum":[18],"rank-1":[20,85],"terms":[21,86],"(where":[22],"each":[23],"term":[24],"is":[25,33],"outer":[27],"product":[28],"vectors).":[30],"This":[31],"also":[34,126],"known":[35],"as":[36],"Parafac":[37],"or":[38],"Candecomp,":[39],"and":[40,69,106,110,112,146,152],"general":[42],"condition":[44,63],"for":[45,77],"was":[46],"obtained":[47,76],"by":[48],"Kruskal":[49],"in":[50,90],"1977":[51],"[Linear":[52],"Algebra":[53],"Appl.,":[54],"18":[55],"(1977),":[56],"pp.":[57],"95\u2013138].":[58],"More":[59],"recently,":[60],"Kruskal\u2019s":[61],"has":[64],"been":[65,75],"generalized":[66],"to":[67,117,139],",":[68,122],"less":[70],"restrictive":[71],"conditions":[73,115,136],"have":[74],"case":[79],"where":[80],"vectors":[82],"are":[87,137],"linearly":[88],"independent":[89],"(at":[91],"least)":[92],"one":[93],"modes.":[96],"consider":[98],"with":[101],"some":[102],"form":[103],"symmetry,":[105],"prove":[107,127],"necessary,":[108],"sufficient,":[109],"necessary":[111],"sufficient":[113],"analogous":[116],"asymmetric":[119,153],"case.":[120],"For":[121],"4,":[123],"5,":[124],"we":[125,142],"generic":[128],"bounds":[130],"on":[131],".":[132],"Most":[133],"these":[135],"easy":[138],"check.":[140],"Throughout,":[141],"emphasize":[143],"analogies":[145],"striking":[147],"differences":[148],"between":[149],"symmetric":[151],"cases.":[154]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
