{"id":"https://openalex.org/W2998798002","doi":"https://doi.org/10.1137/18m1229973","title":"A TT-Based Hierarchical Framework for Decomposing High-Order Tensors","display_name":"A TT-Based Hierarchical Framework for Decomposing High-Order Tensors","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2998798002","doi":"https://doi.org/10.1137/18m1229973","mag":"2998798002"},"language":"en","primary_location":{"id":"doi:10.1137/18m1229973","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1229973","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-02436368","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031572009","display_name":"Yassine Zniyed","orcid":"https://orcid.org/0000-0002-6894-3449"},"institutions":[{"id":"https://openalex.org/I4210097418","display_name":"Laboratoire des signaux et syst\u00e8mes","ror":"https://ror.org/00skw9v43","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I277688954","https://openalex.org/I4210097418","https://openalex.org/I4210107720"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Yassine Zniyed","raw_affiliation_strings":["L2S - Laboratoire des signaux et syst\u00e8mes (Plateau de Moulon 3 rue Joliot Curie 91192 GIF SUR YVETTE CEDEX - France)"],"affiliations":[{"raw_affiliation_string":"L2S - Laboratoire des signaux et syst\u00e8mes (Plateau de Moulon 3 rue Joliot Curie 91192 GIF SUR YVETTE CEDEX - France)","institution_ids":["https://openalex.org/I4210097418"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042386199","display_name":"R\u00e9my Boyer","orcid":"https://orcid.org/0000-0002-7170-350X"},"institutions":[{"id":"https://openalex.org/I4210115519","display_name":"Centre de Recherche en Informatique","ror":"https://ror.org/020cdve92","country_code":"FR","type":"facility","lineage":["https://openalex.org/I190752583","https://openalex.org/I2746051580","https://openalex.org/I4210091621","https://openalex.org/I4210115519","https://openalex.org/I70768539"]},{"id":"https://openalex.org/I2279609970","display_name":"Universit\u00e9 de Lille","ror":"https://ror.org/02kzqn938","country_code":"FR","type":"education","lineage":["https://openalex.org/I2279609970"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"R\u00e9my Boyer","raw_affiliation_strings":["CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (Universit\u00e9 de Lille - Campus scientifique - B\u00e2timent ESPRIT - Avenue Henri Poincar\u00e9 - 59655 Villeneuve d\u2019Ascq - France)"],"affiliations":[{"raw_affiliation_string":"CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (Universit\u00e9 de Lille - Campus scientifique - B\u00e2timent ESPRIT - Avenue Henri Poincar\u00e9 - 59655 Villeneuve d\u2019Ascq - France)","institution_ids":["https://openalex.org/I4210115519","https://openalex.org/I2279609970"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051813339","display_name":"Andr\u00e9 L. F. de Almeida","orcid":"https://orcid.org/0000-0002-3149-6307"},"institutions":[{"id":"https://openalex.org/I4210106479","display_name":"Laboratoire d'Informatique, Signaux et Syst\u00e8mes de Sophia Antipolis","ror":"https://ror.org/01215r597","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I201841394","https://openalex.org/I4210106479","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Andr\u00e9 L. F. de Almeida","raw_affiliation_strings":["Laboratoire d'Informatique, Signaux, et Syst\u00e8mes de Sophia-Antipolis (I3S) / Equipe SIGNAL (France)"],"affiliations":[{"raw_affiliation_string":"Laboratoire d'Informatique, Signaux, et Syst\u00e8mes de Sophia-Antipolis (I3S) / Equipe SIGNAL (France)","institution_ids":["https://openalex.org/I4210106479"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050519323","display_name":"G\u00e9rard Favier","orcid":"https://orcid.org/0000-0002-8882-7410"},"institutions":[{"id":"https://openalex.org/I4210106479","display_name":"Laboratoire d'Informatique, Signaux et Syst\u00e8mes de Sophia Antipolis","ror":"https://ror.org/01215r597","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I201841394","https://openalex.org/I4210106479","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"G\u00e9rard Favier","raw_affiliation_strings":["Laboratoire d'Informatique, Signaux, et Syst\u00e8mes de Sophia-Antipolis (I3S) / Equipe SIGNAL (France)"],"affiliations":[{"raw_affiliation_string":"Laboratoire d'Informatique, Signaux, et Syst\u00e8mes de Sophia-Antipolis (I3S) / Equipe SIGNAL (France)","institution_ids":["https://openalex.org/I4210106479"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5031572009"],"corresponding_institution_ids":["https://openalex.org/I4210097418"],"apc_list":null,"apc_paid":null,"fwci":3.2417,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.94814815,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"42","issue":"2","first_page":"A822","last_page":"A848"},"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":0.9605000019073486,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.7140952348709106},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.700434148311615},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6572035551071167},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.6053010821342468},{"id":"https://openalex.org/keywords/tucker-decomposition","display_name":"Tucker decomposition","score":0.46834227442741394},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.456554114818573},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45237645506858826},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.450916588306427},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.43423378467559814},{"id":"https://openalex.org/keywords/tensor-decomposition","display_name":"Tensor decomposition","score":0.34669917821884155},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.24615532159805298},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.06538465619087219}],"concepts":[{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.7140952348709106},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.700434148311615},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6572035551071167},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.6053010821342468},{"id":"https://openalex.org/C42704193","wikidata":"https://www.wikidata.org/wiki/Q7851097","display_name":"Tucker decomposition","level":4,"score":0.46834227442741394},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.456554114818573},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45237645506858826},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.450916588306427},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.43423378467559814},{"id":"https://openalex.org/C2986737658","wikidata":"https://www.wikidata.org/wiki/Q30103009","display_name":"Tensor decomposition","level":3,"score":0.34669917821884155},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.24615532159805298},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.06538465619087219},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/18m1229973","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1229973","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-02436368v1","is_oa":true,"landing_page_url":"https://hal.science/hal-02436368","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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 Scientific Computing, 2020, 42 (2), pp.A822-A848. &#x27E8;10.1137/18m1229973&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:lilloa.univ-lille.fr:20.500.12210/21961","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.12210/21961","pdf_url":null,"source":{"id":"https://openalex.org/S4306402203","display_name":"LillOA (Universit\u00e9 de Lille (University Of Lille))","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210123514","host_organization_name":"Centre d'Etudes en Civilisations, Langues et Litt\u00e9ratures Etrang\u00e8res","host_organization_lineage":["https://openalex.org/I4210123514"],"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":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-02436368v1","is_oa":true,"landing_page_url":"https://hal.science/hal-02436368","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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 Scientific Computing, 2020, 42 (2), pp.A822-A848. &#x27E8;10.1137/18m1229973&#x27E9;","raw_type":"Journal articles"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W301566927","https://openalex.org/W1682665945","https://openalex.org/W1690316246","https://openalex.org/W1963826206","https://openalex.org/W1967077133","https://openalex.org/W1967538125","https://openalex.org/W1967859589","https://openalex.org/W1971035031","https://openalex.org/W1973615963","https://openalex.org/W1989786408","https://openalex.org/W1990488619","https://openalex.org/W1993482030","https://openalex.org/W1995406764","https://openalex.org/W2000215628","https://openalex.org/W2001518794","https://openalex.org/W2004026774","https://openalex.org/W2011775600","https://openalex.org/W2013912476","https://openalex.org/W2024165284","https://openalex.org/W2030101839","https://openalex.org/W2038198231","https://openalex.org/W2042143333","https://openalex.org/W2051376468","https://openalex.org/W2052856353","https://openalex.org/W2063385922","https://openalex.org/W2074256314","https://openalex.org/W2076028636","https://openalex.org/W2079705627","https://openalex.org/W2081106919","https://openalex.org/W2081962379","https://openalex.org/W2088025933","https://openalex.org/W2088522763","https://openalex.org/W2096699795","https://openalex.org/W2123226256","https://openalex.org/W2132267493","https://openalex.org/W2133512121","https://openalex.org/W2134793668","https://openalex.org/W2150004236","https://openalex.org/W2158071874","https://openalex.org/W2330159389","https://openalex.org/W2344468249","https://openalex.org/W2469230926","https://openalex.org/W2515665519","https://openalex.org/W2531542831","https://openalex.org/W2570391697","https://openalex.org/W2915098601","https://openalex.org/W2943999120","https://openalex.org/W2949757588","https://openalex.org/W2962947392","https://openalex.org/W2962952042","https://openalex.org/W2963242183","https://openalex.org/W3121849872"],"related_works":["https://openalex.org/W3151473062","https://openalex.org/W2891735857","https://openalex.org/W4214526161","https://openalex.org/W47805180","https://openalex.org/W4210544666","https://openalex.org/W2093953080","https://openalex.org/W2564982703","https://openalex.org/W3127610061","https://openalex.org/W2891277085","https://openalex.org/W2347172331"],"abstract_inverted_index":{"In":[0,68,177],"the":[1,40,47,64,73,77,82,85,106,118,175,192,204,223,226],"context":[2,83],"of":[3,17,46,84,109,174,191,225],"big":[4],"data,":[5],"high-order":[6,111],"tensor":[7,23,41,218],"decompositions":[8],"have":[9],"to":[10,63,104,166,172,211],"face":[11],"a":[12,28,56,89,102,110,125,130,154,159,184],"new":[13,90,114,155],"challenge":[14],"in":[15,55,81,124],"terms":[16],"storage":[18,35],"and":[19,50,121,134,158,201,207,220],"computational":[20],"costs.":[21],"The":[22,44,113,150],"train":[24],"(TT)":[25],"decomposition":[26,80,108],"provides":[27],"very":[29,143],"useful":[30],"graph-based":[31],"model":[32],"reduction,":[33],"whose":[34],"cost":[36],"grows":[37],"linearly":[38],"with":[39,147,168],"order":[42],"$D$.":[43],"computation":[45],"TT-core":[48,119,208],"tensors":[49,120,209],"TT-ranks":[51,123,206],"can":[52],"be":[53],"done":[54],"stable":[57,131],"sequential":[58],"(i.e.,":[59,132],"noniterative)":[60,133],"way":[61],"thanks":[62],"popular":[65],"TT-SVD":[66,200],"algorithm.":[67,228],"this":[69],"paper,":[70],"we":[71],"exploit":[72],"ideas":[74],"developed":[75],"for":[76,183,216],"hierarchical/tree":[78],"Tucker":[79],"TT":[86,107],"decomposition.":[87],"Specifically,":[88],"efficient":[91,137],"estimation":[92],"scheme,":[93],"called":[94],"TT-HSVD":[95,151,179,202],"(Tensor-Train":[96],"Hierarchical":[97],"SVD),":[98],"is":[99,129,142,180,195],"proposed":[100,227],"as":[101],"solution":[103],"compute":[105,203],"tensor.":[112],"algorithm":[115,138,152],"simultaneously":[116],"delivers":[117],"their":[122],"hierarchical":[126],"way.":[127],"It":[128],"computationally":[135],"more":[136],"than":[139],"TT-SVD,":[140],"which":[141,163],"important":[144],"when":[145],"dealing":[146],"large-scale":[148],"data.":[149],"uses":[153],"reshaping":[156],"strategy":[157],"tailored":[160],"partial":[161],"SVD,":[162],"allows":[164],"us":[165],"deal":[167],"smaller":[169],"matrices":[170],"compared":[171],"those":[173],"TT-SVD.":[176],"addition,":[178],"well":[181],"suited":[182],"parallel":[185],"processing":[186],"architecture.":[187],"An":[188],"algebraic":[189],"analysis":[190],"two":[193],"algorithms":[194],"carried":[196],"out,":[197],"showing":[198],"that":[199],"same":[205],"up":[210],"specific":[212],"bases.":[213],"Simulation":[214],"results":[215],"different":[217],"orders":[219],"dimensions":[221],"corroborate":[222],"effectiveness":[224]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":5}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
