{"id":"https://openalex.org/W4214916906","doi":"https://doi.org/10.1137/20m1381046","title":"Guarantees for Existence of a Best Canonical Polyadic Approximation of a Noisy Low-Rank Tensor","display_name":"Guarantees for Existence of a Best Canonical Polyadic Approximation of a Noisy Low-Rank Tensor","publication_year":2022,"publication_date":"2022-03-01","ids":{"openalex":"https://openalex.org/W4214916906","doi":"https://doi.org/10.1137/20m1381046"},"language":"en","primary_location":{"id":"doi:10.1137/20m1381046","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1381046","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/20.500.12942/686145","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017164422","display_name":"Eric Evert","orcid":"https://orcid.org/0000-0002-5488-8725"},"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":"Eric Evert","raw_affiliation_strings":["KU Leuven, Dept. of Electrical Engineering ESAT/STADIUS, Kasteelpark Arenberg 10, bus 2446, B-3001 Leuven, Belgium"],"raw_orcid":"https://orcid.org/0000-0002-5488-8725","affiliations":[{"raw_affiliation_string":"KU Leuven, Dept. of Electrical Engineering ESAT/STADIUS, Kasteelpark Arenberg 10, bus 2446, B-3001 Leuven, Belgium","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":["KU Leuven, Dept. of Electrical Engineering ESAT/STADIUS, Kasteelpark Arenberg 10, bus 2446, B-3001 Leuven, Belgium"],"raw_orcid":"https://orcid.org/0000-0001-5562-5014","affiliations":[{"raw_affiliation_string":"KU Leuven, Dept. of Electrical Engineering ESAT/STADIUS, Kasteelpark Arenberg 10, bus 2446, B-3001 Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5017164422"],"corresponding_institution_ids":["https://openalex.org/I99464096"],"apc_list":null,"apc_paid":null,"fwci":0.6834,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.64268585,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"43","issue":"1","first_page":"328","last_page":"369"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9677000045776367,"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/mathematics","display_name":"Mathematics","score":0.7898322343826294},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7035062909126282},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6927067637443542},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.6487237215042114},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5190173387527466},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.45156481862068176},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4464068114757538},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.27497512102127075},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07943978905677795},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.066497802734375}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7898322343826294},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7035062909126282},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6927067637443542},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.6487237215042114},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5190173387527466},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.45156481862068176},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4464068114757538},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.27497512102127075},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07943978905677795},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.066497802734375},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/20m1381046","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1381046","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:20.500.12942/686145","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/20.500.12942/686145","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. 43 (1), (328-369)","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:lirias2repo.kuleuven.be:20.500.12942/686145","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/20.500.12942/686145","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. 43 (1), (328-369)","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1371775621","display_name":null,"funder_award_id":"C16/15/059","funder_id":"https://openalex.org/F4320322308","funder_display_name":"KU Leuven"},{"id":"https://openalex.org/G6044690702","display_name":null,"funder_award_id":"30468160 (SeLMA)","funder_id":"https://openalex.org/F4320321390","funder_display_name":"Fonds De La Recherche Scientifique - FNRS"},{"id":"https://openalex.org/G8739552135","display_name":null,"funder_award_id":"3E190402","funder_id":"https://openalex.org/F4320322308","funder_display_name":"KU Leuven"}],"funders":[{"id":"https://openalex.org/F4320321390","display_name":"Fonds De La Recherche Scientifique - FNRS","ror":"https://ror.org/03q83t159"},{"id":"https://openalex.org/F4320322308","display_name":"KU Leuven","ror":"https://ror.org/05f950310"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W1754171797","https://openalex.org/W1974785908","https://openalex.org/W2001916104","https://openalex.org/W2013912476","https://openalex.org/W2015211035","https://openalex.org/W2019219605","https://openalex.org/W2024165284","https://openalex.org/W2027201767","https://openalex.org/W2049518738","https://openalex.org/W2057069782","https://openalex.org/W2057503509","https://openalex.org/W2065931606","https://openalex.org/W2072139290","https://openalex.org/W2076603483","https://openalex.org/W2079705627","https://openalex.org/W2092978222","https://openalex.org/W2105050479","https://openalex.org/W2112702842","https://openalex.org/W2119412403","https://openalex.org/W2125880378","https://openalex.org/W2132220618","https://openalex.org/W2132267493","https://openalex.org/W2150059498","https://openalex.org/W2156982859","https://openalex.org/W2172195418","https://openalex.org/W2291029025","https://openalex.org/W2316966455","https://openalex.org/W2421281141","https://openalex.org/W2469230926","https://openalex.org/W2784159064","https://openalex.org/W2890058448","https://openalex.org/W2962827512","https://openalex.org/W2963117880","https://openalex.org/W2963725088","https://openalex.org/W3037004955","https://openalex.org/W3102183770","https://openalex.org/W3123517045","https://openalex.org/W4205696294","https://openalex.org/W4251986282"],"related_works":["https://openalex.org/W2391023104","https://openalex.org/W2569661359","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/W2216309014","https://openalex.org/W4290987221"],"abstract_inverted_index":{"The":[0,257],"canonical":[1,130],"polyadic":[2,131],"decomposition":[3,161],"(CPD)":[4],"of":[5,24,64,86,95,124,141,154,193,205,232,255,260,268],"a":[6,10,42,48,76,96,128,139,163,177,228,245,266],"low-rank":[7,34,66,159,178,207,234],"tensor":[8,43,67,77,122,160,179,238],"plays":[9],"major":[11],"role":[12],"in":[13,104,144,190],"data":[14],"analysis":[15],"and":[16,148,195,236],"signal":[17],"processing":[18],"by":[19,212,265],"allowing":[20],"for":[21,61,198,203,217,253],"unique":[22,129],"recovery":[23],"underlying":[25],"factors.":[26],"However,":[27],"it":[28],"is":[29,38,188],"well":[30],"known":[31],"that":[32,118],"the":[33,62,93,191,218,237,261],"CPD":[35,52,146],"approximation":[36,53,147],"problem":[37],"ill-posed.":[39],"That":[40],"is,":[41],"may":[44,135],"fail":[45],"to":[46,112],"have":[47],"best":[49,65,106,206,233],"rank":[50,87,182,187],"$R$":[51,108,121],"when":[54],"$R>1$.":[55],"This":[56,133],"article":[57,262],"gives":[58],"deterministic":[59],"bounds":[60],"existence":[63,204,231],"approximations":[68,109,208,235],"over":[69],"${\\mathbb{K}}={\\mathbb{R}}$":[70],"or":[71],"${\\mathbb{K}}={\\mathbb{C}}$.":[72],"More":[73],"precisely,":[74],"given":[75],"${\\mathcal":[78,102],"T}":[79],"\\in":[80],"{\\mathbb{K}}^{I":[81],"\\times":[82,84],"I":[83],"I}$":[85],"$R":[88],"\\leq":[89],"I$,":[90],"we":[91,116,157,171,226,243],"compute":[92],"radius":[94],"Frobenius":[97],"norm":[98],"ball":[99,126],"centered":[100],"at":[101],"T}$":[103],"which":[105,145,180,249],"${\\mathbb{K}}$-rank":[107,120],"are":[110,150,209,263],"guaranteed":[111],"exist.":[113],"In":[114,152,223,241],"addition":[115,242],"show":[117,172],"every":[119],"inside":[123],"this":[125,169,224],"has":[127,181],"decomposition.":[132],"neighborhood":[134,140],"be":[136],"interpreted":[137],"as":[138,162],"\u201cmathematical":[142],"truth\"":[143],"computation":[149],"well-posed.":[151],"pursuit":[153],"these":[155],"bounds,":[156],"describe":[158],"\u201cjoint":[164],"generalized":[165,200,220],"eigenvalue\"":[166],"problem.":[167,222],"Using":[168],"framework,":[170],"that,":[173],"under":[174],"mild":[175],"assumptions,":[176],"strictly":[183],"greater":[184],"than":[185],"border":[186],"defective":[189],"sense":[192],"algebraic":[194],"geometric":[196],"multiplicities":[197],"joint":[199,219],"eigenvalues.":[201],"Bounds":[202],"then":[210],"obtained":[211],"establishing":[213],"perturbation":[214],"theoretic":[215],"results":[216,259],"eigenvalue":[221],"way":[225],"establish":[227],"connection":[229],"between":[230],"spectral":[239],"norm.":[240],"solve":[244],"\u201ctensor":[246],"Procrustes":[247],"problem\"":[248],"examines":[250],"orthogonal":[251],"compressions":[252],"pairs":[254],"tensors.":[256],"main":[258],"illustrated":[264],"variety":[267],"numerical":[269],"experiments.":[270]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
