{"id":"https://openalex.org/W2965565138","doi":"https://doi.org/10.1137/17m1140790","title":"Fiber Sampling Approach to Canonical Polyadic Decomposition and Application to Tensor Completion","display_name":"Fiber Sampling Approach to Canonical Polyadic Decomposition and Application to Tensor Completion","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2965565138","doi":"https://doi.org/10.1137/17m1140790","mag":"2965565138"},"language":"en","primary_location":{"id":"doi:10.1137/17m1140790","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1140790","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/123456789/639687","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/I4210104270","display_name":"McCormick (United States)","ror":"https://ror.org/01ftbgh03","country_code":"US","type":"company","lineage":["https://openalex.org/I4210104270"]},{"id":"https://openalex.org/I51556381","display_name":"University of Virginia","ror":"https://ror.org/0153tk833","country_code":"US","type":"education","lineage":["https://openalex.org/I51556381"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mikael S\u00f8rensen","raw_affiliation_strings":["University of Virginia, Department of Electrical and Computer Engineering, Thornton Hall, 351 McCormick Road, Charlottesville, Virginia 22904, USA,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Virginia, Department of Electrical and Computer Engineering, Thornton Hall, 351 McCormick Road, Charlottesville, Virginia 22904, USA,","institution_ids":["https://openalex.org/I51556381","https://openalex.org/I4210104270"]}]},{"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":true,"raw_author_name":"Lieven De Lathauwer","raw_affiliation_strings":["KU Leuven-Kulak, E. Sabbelaan 53, 8500 Kortrijk, Belgium,","KU Leuven -E.E. Dept. (ESAT) -STADIUS Center for Dynamical Systems, Signal Processing and Data Analytics, Kasteelpark Arenberg 10, B-3001 Leuven-Heverlee, Belgium, and the Group Science, Engineering and Technology,"],"raw_orcid":"https://orcid.org/0000-0001-5562-5014","affiliations":[{"raw_affiliation_string":"KU Leuven-Kulak, E. Sabbelaan 53, 8500 Kortrijk, Belgium,","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"KU Leuven -E.E. Dept. (ESAT) -STADIUS Center for Dynamical Systems, Signal Processing and Data Analytics, Kasteelpark Arenberg 10, B-3001 Leuven-Heverlee, Belgium, and the Group Science, Engineering and Technology,","institution_ids":["https://openalex.org/I99464096"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5009006026"],"corresponding_institution_ids":["https://openalex.org/I99464096"],"apc_list":null,"apc_paid":null,"fwci":3.238,"has_fulltext":false,"cited_by_count":42,"citation_normalized_percentile":{"value":0.92892157,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"40","issue":"3","first_page":"888","last_page":"917"},"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/T10305","display_name":"Power System Optimization and Stability","score":0.9577000141143799,"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"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9552000164985657,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.7268991470336914},{"id":"https://openalex.org/keywords/multilinear-map","display_name":"Multilinear map","score":0.5971468091011047},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5671417117118835},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5175904035568237},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.48106932640075684},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4639320969581604},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.45949697494506836},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4567282795906067},{"id":"https://openalex.org/keywords/signal-processing","display_name":"Signal processing","score":0.4561857283115387},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4410075843334198},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.4184938371181488},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4000418782234192},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3745768666267395},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.353478342294693},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.16779157519340515},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15289321541786194},{"id":"https://openalex.org/keywords/digital-signal-processing","display_name":"Digital signal processing","score":0.14699119329452515}],"concepts":[{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.7268991470336914},{"id":"https://openalex.org/C84392682","wikidata":"https://www.wikidata.org/wiki/Q1952404","display_name":"Multilinear map","level":2,"score":0.5971468091011047},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5671417117118835},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5175904035568237},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.48106932640075684},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4639320969581604},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.45949697494506836},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4567282795906067},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.4561857283115387},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4410075843334198},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4184938371181488},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4000418782234192},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3745768666267395},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.353478342294693},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.16779157519340515},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15289321541786194},{"id":"https://openalex.org/C84462506","wikidata":"https://www.wikidata.org/wiki/Q173142","display_name":"Digital signal processing","level":2,"score":0.14699119329452515},{"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/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/17m1140790","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1140790","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:123456789/639687","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/639687","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"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. 40 (3), Art.No. 3, (888-917)","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/639687","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/639687","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"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. 40 (3), Art.No. 3, (888-917)","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2002407387","display_name":null,"funder_award_id":"G.0F67.18N","funder_id":"https://openalex.org/F4320321730","funder_display_name":"Fonds Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G4049749074","display_name":null,"funder_award_id":"339804","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"},{"id":"https://openalex.org/G6044513077","display_name":null,"funder_award_id":"C16/15/059-nD","funder_id":"https://openalex.org/F4320322681","funder_display_name":"Onderzoeksraad, KU Leuven"}],"funders":[{"id":"https://openalex.org/F4320321730","display_name":"Fonds Wetenschappelijk Onderzoek","ror":"https://ror.org/03qtxy027"},{"id":"https://openalex.org/F4320322681","display_name":"Onderzoeksraad, KU Leuven","ror":"https://ror.org/05f950310"},{"id":"https://openalex.org/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W1562564874","https://openalex.org/W1814521481","https://openalex.org/W1885765327","https://openalex.org/W1970195563","https://openalex.org/W1972547249","https://openalex.org/W1974785908","https://openalex.org/W1979750072","https://openalex.org/W2000045479","https://openalex.org/W2000215628","https://openalex.org/W2004658690","https://openalex.org/W2008560788","https://openalex.org/W2024166170","https://openalex.org/W2027201767","https://openalex.org/W2029563140","https://openalex.org/W2033154334","https://openalex.org/W2038920431","https://openalex.org/W2056649499","https://openalex.org/W2057503509","https://openalex.org/W2063948774","https://openalex.org/W2070013413","https://openalex.org/W2078291856","https://openalex.org/W2078677240","https://openalex.org/W2105186495","https://openalex.org/W2117756735","https://openalex.org/W2118550318","https://openalex.org/W2119340035","https://openalex.org/W2119412403","https://openalex.org/W2141280932","https://openalex.org/W2157615762","https://openalex.org/W2166313513","https://openalex.org/W2170668800","https://openalex.org/W2195165862","https://openalex.org/W2227958069","https://openalex.org/W2469230926","https://openalex.org/W2529568750","https://openalex.org/W2529588774","https://openalex.org/W2611328865","https://openalex.org/W2802039202","https://openalex.org/W2915098601","https://openalex.org/W2964313686","https://openalex.org/W3098973674","https://openalex.org/W3102183770","https://openalex.org/W4242200182","https://openalex.org/W4251986282"],"related_works":["https://openalex.org/W1999178348","https://openalex.org/W4296311369","https://openalex.org/W2922481674","https://openalex.org/W3193555930","https://openalex.org/W1572092093","https://openalex.org/W1570745949","https://openalex.org/W2893527900","https://openalex.org/W3043534693","https://openalex.org/W3177385724","https://openalex.org/W2535617683"],"abstract_inverted_index":{"Tensor":[0],"decompositions":[1],"play":[2],"an":[3,53,132],"important":[4],"role":[5],"in":[6,143,163],"a":[7,93,105,144],"variety":[8],"of":[9,60,69,83,92,140,146,198,201],"applications,":[10],"such":[11],"as":[12,72,74],"signal":[13,150],"processing":[14,148,151],"and":[15,33,149],"machine":[16],"learning.":[17],"In":[18,39],"practice,":[19],"the":[20,45,58,81,90,111,114,121,167,183,196,199],"tensor":[21,37,94,177],"can":[22],"be":[23,139],"incomplete":[24,202],"or":[25],"very":[26],"large,":[27],"making":[28],"it":[29],"difficult":[30],"to":[31,98,119,138,165],"analyze":[32],"process":[34],"using":[35],"conventional":[36],"techniques.":[38],"this":[40],"paper":[41],"we":[42,88],"focus":[43],"on":[44],"basic":[46],"canonical":[47],"polyadic":[48],"decomposition":[49,108],"(CPD).":[50],"We":[51],"propose":[52],"algebraic":[54,71,184],"framework":[55,185],"for":[56,80,174,195],"finding":[57],"CPD":[59,82,91,200],"tensors":[61],"that":[62,135,157,182],"have":[63],"missing":[64,96],"fibers.":[65],"This":[66,169],"includes":[67],"extensions":[68],"multilinear":[70],"well":[73],"generic":[75],"uniqueness":[76],"conditions":[77],"originally":[78],"developed":[79],"fully":[84],"observed":[85],"tensors.":[86,205],"Computationally,":[87],"reduce":[89],"with":[95,128],"fibers":[97,160],"relatively":[99,158],"simple":[100],"matrix":[101,106],"completion":[102],"problems":[103],"via":[104],"eigenvalue":[107],"(EVD).":[109],"Under":[110],"given":[112],"conditions,":[113],"EVD-based":[115],"algorithm":[116],"is":[117],"guaranteed":[118],"return":[120],"exact":[122],"CPD.":[123,168],"The":[124],"derivation":[125],"establishes":[126],"connections":[127],"so-called":[129],"coupled":[130],"CPDs,":[131],"emerging":[133],"concept":[134],"has":[136],"proven":[137],"great":[141],"interest":[142],"range":[145],"array":[147],"applications.":[152],"It":[153],"will":[154],"become":[155],"clear":[156],"few":[159],"are":[161],"needed":[162],"order":[164],"compute":[166],"makes":[170],"fiber":[171],"sampling":[172],"interesting":[173],"large":[175],"scale":[176],"decompositions.":[178],"Numerical":[179],"experiments":[180],"show":[181],"may":[186],"significantly":[187],"speed":[188],"up":[189],"more":[190],"common":[191],"optimization-based":[192],"computation":[193],"schemes":[194],"estimation":[197],"noisy":[203],"data":[204]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":12},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":1}],"updated_date":"2026-06-25T08:15:23.626066","created_date":"2019-08-13T00:00:00"}
