{"id":"https://openalex.org/W2982082907","doi":"https://doi.org/10.23919/eusipco.2019.8902781","title":"Detecting the Rank of a Symmetric Tensor","display_name":"Detecting the Rank of a Symmetric Tensor","publication_year":2019,"publication_date":"2019-09-01","ids":{"openalex":"https://openalex.org/W2982082907","doi":"https://doi.org/10.23919/eusipco.2019.8902781","mag":"2982082907"},"language":"en","primary_location":{"id":"doi:10.23919/eusipco.2019.8902781","is_oa":false,"landing_page_url":"https://doi.org/10.23919/eusipco.2019.8902781","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 27th European Signal Processing Conference (EUSIPCO)","raw_type":"proceedings-article"},"type":"preprint","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/A5057722199","display_name":"Arthur Marmin","orcid":"https://orcid.org/0000-0002-2508-6969"},"institutions":[{"id":"https://openalex.org/I4210107720","display_name":"CentraleSup\u00e9lec","ror":"https://ror.org/019tcpt25","country_code":"FR","type":"facility","lineage":["https://openalex.org/I277688954","https://openalex.org/I4210107720"]},{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Arthur Marmin","raw_affiliation_strings":["Center for Visual Computing, CentraleSup\u00e9lec, INRIA, Universit\u00e9Paris-Saclay, Gif-sur-Yvette, France"],"affiliations":[{"raw_affiliation_string":"Center for Visual Computing, CentraleSup\u00e9lec, INRIA, Universit\u00e9Paris-Saclay, Gif-sur-Yvette, France","institution_ids":["https://openalex.org/I4210107720","https://openalex.org/I1326498283","https://openalex.org/I277688954"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029500996","display_name":"Marc Castella","orcid":"https://orcid.org/0000-0003-0690-3676"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210145102","display_name":"Institut Polytechnique de Paris","ror":"https://ror.org/042tfbd02","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Marc Castella","raw_affiliation_strings":["SAMOVAR, CNRS, T\u00e9l\u00e9com SudParis, Institut Polytechnique de Paris, Evry, France"],"affiliations":[{"raw_affiliation_string":"SAMOVAR, CNRS, T\u00e9l\u00e9com SudParis, Institut Polytechnique de Paris, Evry, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210145102"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062845079","display_name":"Jean\u2010Christophe Pesquet","orcid":"https://orcid.org/0000-0002-5943-8061"},"institutions":[{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]},{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210107720","display_name":"CentraleSup\u00e9lec","ror":"https://ror.org/019tcpt25","country_code":"FR","type":"facility","lineage":["https://openalex.org/I277688954","https://openalex.org/I4210107720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jean-Christophe Pesquet","raw_affiliation_strings":["Center for Visual Computing, CentraleSup\u00e9lec, INRIA, Universit\u00e9Paris-Saclay, Gif-sur-Yvette, France"],"affiliations":[{"raw_affiliation_string":"Center for Visual Computing, CentraleSup\u00e9lec, INRIA, Universit\u00e9Paris-Saclay, Gif-sur-Yvette, France","institution_ids":["https://openalex.org/I4210107720","https://openalex.org/I1326498283","https://openalex.org/I277688954"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5057722199"],"corresponding_institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I277688954","https://openalex.org/I4210107720"],"apc_list":null,"apc_paid":null,"fwci":0.2942,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.46520147,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"5"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":1.0,"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":1.0,"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9771999716758728,"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"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9670000076293945,"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/rank","display_name":"Rank (graph theory)","score":0.8483883142471313},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.7327855229377747},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6044882535934448},{"id":"https://openalex.org/keywords/symmetric-tensor","display_name":"Symmetric tensor","score":0.5741947293281555},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.5185832977294922},{"id":"https://openalex.org/keywords/tucker-decomposition","display_name":"Tucker decomposition","score":0.514495849609375},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.4676828980445862},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.4243814945220947},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3748510479927063},{"id":"https://openalex.org/keywords/tensor-decomposition","display_name":"Tensor decomposition","score":0.37392961978912354},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3721301257610321},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33281782269477844},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.320054829120636},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.31579160690307617},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.24401769042015076},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.23422753810882568},{"id":"https://openalex.org/keywords/exact-solutions-in-general-relativity","display_name":"Exact solutions in general relativity","score":0.23369097709655762},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16986504197120667},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16402941942214966},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.15021023154258728},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05922076106071472}],"concepts":[{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.8483883142471313},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.7327855229377747},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6044882535934448},{"id":"https://openalex.org/C20178491","wikidata":"https://www.wikidata.org/wiki/Q2204117","display_name":"Symmetric tensor","level":3,"score":0.5741947293281555},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.5185832977294922},{"id":"https://openalex.org/C42704193","wikidata":"https://www.wikidata.org/wiki/Q7851097","display_name":"Tucker decomposition","level":4,"score":0.514495849609375},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.4676828980445862},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4243814945220947},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3748510479927063},{"id":"https://openalex.org/C2986737658","wikidata":"https://www.wikidata.org/wiki/Q30103009","display_name":"Tensor decomposition","level":3,"score":0.37392961978912354},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3721301257610321},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33281782269477844},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.320054829120636},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31579160690307617},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.24401769042015076},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.23422753810882568},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.23369097709655762},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16986504197120667},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16402941942214966},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.15021023154258728},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05922076106071472},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0},{"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:10.23919/eusipco.2019.8902781","is_oa":false,"landing_page_url":"https://doi.org/10.23919/eusipco.2019.8902781","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 27th European Signal Processing Conference (EUSIPCO)","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:hal-02284991v1","is_oa":false,"landing_page_url":"https://hal.science/hal-02284991","pdf_url":null,"source":{"id":"https://openalex.org/S4406922461","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"EUSIPCO 2019 - 27th European Signal Processing Conference, Sep 2019, Coru\u00f1a, Spain. pp.1-5","raw_type":"Conference papers"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W792141054","https://openalex.org/W1652247329","https://openalex.org/W1755563775","https://openalex.org/W1991386947","https://openalex.org/W2007715285","https://openalex.org/W2024165284","https://openalex.org/W2033693394","https://openalex.org/W2039748980","https://openalex.org/W2061186416","https://openalex.org/W2071729267","https://openalex.org/W2079705627","https://openalex.org/W2105724942","https://openalex.org/W2118550318","https://openalex.org/W2245131330","https://openalex.org/W2469230926","https://openalex.org/W2794566895","https://openalex.org/W2963492625","https://openalex.org/W4210921079","https://openalex.org/W6637079763","https://openalex.org/W6676039487"],"related_works":["https://openalex.org/W2897298721","https://openalex.org/W2950186459","https://openalex.org/W2216309014","https://openalex.org/W2235665432","https://openalex.org/W2891735857","https://openalex.org/W2569661359","https://openalex.org/W47805180","https://openalex.org/W2093953080","https://openalex.org/W3127610061","https://openalex.org/W2891277085"],"abstract_inverted_index":{"This":[0],"paper":[1],"deals":[2],"with":[3,91,95,117],"the":[4,23,26,29,35,53,61,78,81,84,123,139,144],"problem":[5,64,69],"of":[6,11,25,28,37,55,80,86,125,132,149],"Canonical":[7],"Polyadic":[8],"(CP)":[9],"decomposition":[10,20,63],"a":[12,38,49,56,66,73,99,146],"given":[13,39],"tensor.":[14,58],"Standard":[15],"algorithms":[16],"to":[17,51,76,111],"perform":[18],"this":[19,45,102],"generally":[21,42],"require":[22],"knowledge":[24],"rank":[27,36,54,79,85,96,114,141],"sought":[30],"tensor":[31,40,82],"decomposition.":[32],"Yet,":[33],"determining":[34],"is":[41,105],"hard.":[43],"In":[44],"paper,":[46],"we":[47,71,109],"propose":[48,110],"method":[50,137],"find":[52],"symmetric":[57],"We":[59],"reformulate":[60],"CP":[62],"into":[65],"truncated":[67],"moment":[68,88],"and":[70,128],"derive":[72],"sufficient":[74,103],"condition":[75,104],"certify":[77],"from":[83],"some":[87],"matrices":[89],"associated":[90],"it.":[92],"For":[93],"tensors":[94],"not":[97],"exceeding":[98],"prescribed":[100],"value,":[101],"also":[106],"necessary.":[107],"Finally,":[108],"combine":[112],"our":[113,126],"detection":[115],"procedure":[116],"existing":[118],"algorithms.":[119],"Experimental":[120],"results":[121,127],"show":[122],"validity":[124],"provide":[129],"an":[130],"illustration":[131],"its":[133],"practical":[134],"use.":[135],"Our":[136],"provides":[138],"correct":[140],"even":[142],"in":[143],"presence":[145],"moderate":[147],"level":[148],"noise.":[150]},"counts_by_year":[{"year":2020,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
