{"id":"https://openalex.org/W3135863364","doi":"https://doi.org/10.1137/20m1323266","title":"Triple Decomposition and Tensor Recovery of Third Order Tensors","display_name":"Triple Decomposition and Tensor Recovery of Third Order Tensors","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3135863364","doi":"https://doi.org/10.1137/20m1323266","mag":"3135863364"},"language":"en","primary_location":{"id":"doi:10.1137/20m1323266","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1323266","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011886900","display_name":"Liqun Qi","orcid":"https://orcid.org/0000-0002-1112-5250"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Liqun Qi","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101444632","display_name":"Yannan Chen","orcid":"https://orcid.org/0000-0002-3121-3602"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yannan Chen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080893953","display_name":"Mayank Bakshi","orcid":"https://orcid.org/0000-0002-6051-923X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mayank Bakshi","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5060024086","display_name":"Xinzhen Zhang","orcid":"https://orcid.org/0000-0001-7498-6616"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xinzhen Zhang","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5011886900"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.471,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.9022646,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"42","issue":"1","first_page":"299","last_page":"329"},"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/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.9358999729156494,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9092000126838684,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/tucker-decomposition","display_name":"Tucker decomposition","score":0.8174050450325012},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7562837600708008},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.7304502725601196},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6932841539382935},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.5987024307250977},{"id":"https://openalex.org/keywords/symmetric-tensor","display_name":"Symmetric tensor","score":0.5804038047790527},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4641479253768921},{"id":"https://openalex.org/keywords/third-order","display_name":"Third order","score":0.46121275424957275},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.437496542930603},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39814841747283936},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31091055274009705},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.28605902194976807},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2478058934211731},{"id":"https://openalex.org/keywords/tensor-decomposition","display_name":"Tensor decomposition","score":0.19928580522537231},{"id":"https://openalex.org/keywords/exact-solutions-in-general-relativity","display_name":"Exact solutions in general relativity","score":0.1914862096309662},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.07033106684684753}],"concepts":[{"id":"https://openalex.org/C42704193","wikidata":"https://www.wikidata.org/wiki/Q7851097","display_name":"Tucker decomposition","level":4,"score":0.8174050450325012},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7562837600708008},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.7304502725601196},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6932841539382935},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.5987024307250977},{"id":"https://openalex.org/C20178491","wikidata":"https://www.wikidata.org/wiki/Q2204117","display_name":"Symmetric tensor","level":3,"score":0.5804038047790527},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4641479253768921},{"id":"https://openalex.org/C2777566824","wikidata":"https://www.wikidata.org/wiki/Q1259252","display_name":"Third order","level":2,"score":0.46121275424957275},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.437496542930603},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39814841747283936},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31091055274009705},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.28605902194976807},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2478058934211731},{"id":"https://openalex.org/C2986737658","wikidata":"https://www.wikidata.org/wiki/Q30103009","display_name":"Tensor decomposition","level":3,"score":0.19928580522537231},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.1914862096309662},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.07033106684684753},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C27206212","wikidata":"https://www.wikidata.org/wiki/Q34178","display_name":"Theology","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/20m1323266","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1323266","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3400913060","display_name":null,"funder_award_id":"11871369","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1814521481","https://openalex.org/W1968154520","https://openalex.org/W1992426838","https://openalex.org/W2000045479","https://openalex.org/W2013912476","https://openalex.org/W2021361347","https://openalex.org/W2024165284","https://openalex.org/W2073382079","https://openalex.org/W2078853581","https://openalex.org/W2079731430","https://openalex.org/W2129732816","https://openalex.org/W2166135831","https://openalex.org/W2762772695","https://openalex.org/W2806735006","https://openalex.org/W2963785028"],"related_works":["https://openalex.org/W2897298721","https://openalex.org/W2950186459","https://openalex.org/W2216309014","https://openalex.org/W2235665432","https://openalex.org/W2569661359","https://openalex.org/W3019188729","https://openalex.org/W3137757612","https://openalex.org/W3023133236","https://openalex.org/W2982082907","https://openalex.org/W2140205332"],"abstract_inverted_index":{"Motivated":[0],"by":[1],"the":[2,42,46,49,64,68,76,86,146],"Tucker":[3,69,91],"decomposition,":[4,44],"in":[5,75,93],"this":[6,149],"paper":[7],"we":[8],"introduce":[9],"a":[10,20,40,56],"new":[11],"tensor":[12,23,32,59,108,125],"decomposition":[13,41,82,92,133],"for":[14],"third":[15,21,26,57,106],"order":[16,22,27,58,107],"tensors,":[17],"which":[18],"decomposes":[19],"to":[24],"three":[25],"factor":[28,31],"tensors.":[29],"Each":[30],"has":[33],"two":[34],"low":[35,121,130],"dimensions.":[36],"We":[37],"call":[38],"such":[39,113],"triple":[43,50,53,81,122,132],"and":[45,117,138],"corresponding":[47],"rank":[48,54,131],"rank.":[51,70],"The":[52,71,96],"of":[55,67,73,79,88,90,120,148],"is":[60,83,99,134],"not":[61],"greater":[62],"than":[63,85],"middle":[65],"value":[66],"number":[72,87],"parameters":[74,89],"bilevel":[77],"form":[78],"standard":[80],"less":[84],"substantial":[94],"cases.":[95],"theoretical":[97],"discovery":[98],"confirmed":[100],"numerically.":[101],"Numerical":[102,143],"tests":[103],"show":[104],"that":[105],"data":[109],"from":[110],"practical":[111],"applications":[112],"as":[114],"internet":[115],"traffic":[116],"image":[118],"are":[119,141],"ranks.":[123],"A":[124],"recovery":[126],"method":[127],"based":[128],"on":[129],"proposed.":[135],"Its":[136],"convergence":[137,139],"rate":[140],"established.":[142],"experiments":[144],"confirm":[145],"efficiency":[147],"method.":[150]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1}],"updated_date":"2026-03-05T09:29:38.588285","created_date":"2025-10-10T00:00:00"}
