{"id":"https://openalex.org/W2127114523","doi":"https://doi.org/10.1109/tit.2010.2048466","title":"Dictionary Identification\u2014Sparse Matrix-Factorization via $\\ell_1$-Minimization","display_name":"Dictionary Identification\u2014Sparse Matrix-Factorization via $\\ell_1$-Minimization","publication_year":2010,"publication_date":"2010-06-23","ids":{"openalex":"https://openalex.org/W2127114523","doi":"https://doi.org/10.1109/tit.2010.2048466","mag":"2127114523"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2010.2048466","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2010.2048466","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-00541297","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041230403","display_name":"R\u00e9mi Gribonval","orcid":"https://orcid.org/0000-0002-9450-8125"},"institutions":[{"id":"https://openalex.org/I2802519937","display_name":"Institut de Recherche en Informatique et Syst\u00e8mes Al\u00e9atoires","ror":"https://ror.org/00myn0z94","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I205703379","https://openalex.org/I2802204017","https://openalex.org/I2802519937","https://openalex.org/I28221208","https://openalex.org/I4210127572","https://openalex.org/I4210159245","https://openalex.org/I56067802"]},{"id":"https://openalex.org/I4210112279","display_name":"Milieux environnementaux, transferts et interactions dans les hydrosyst\u00e8mes et les sols","ror":"https://ror.org/0229z0679","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I159885104","https://openalex.org/I2746051580","https://openalex.org/I39804081","https://openalex.org/I4210107625","https://openalex.org/I4210112279"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Remi Gribonval","raw_affiliation_strings":["IRISA, Rennes, Bretagne, FR","Project METISS, IRISA, Rennes, France"],"affiliations":[{"raw_affiliation_string":"IRISA, Rennes, Bretagne, FR","institution_ids":["https://openalex.org/I2802519937"]},{"raw_affiliation_string":"Project METISS, IRISA, Rennes, France","institution_ids":["https://openalex.org/I2802519937","https://openalex.org/I4210112279"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011615599","display_name":"Karin Schnass","orcid":"https://orcid.org/0000-0002-4873-5570"},"institutions":[{"id":"https://openalex.org/I4210158379","display_name":"Johann Radon Institute for Computational and Applied Mathematics","ror":"https://ror.org/05a94k872","country_code":"AT","type":"facility","lineage":["https://openalex.org/I138211613","https://openalex.org/I4210158379"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Karin Schnass","raw_affiliation_strings":["Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz, Austria","Johann Radon Inst. for Comput. & Appl. Math. (RICAM), Linz, Austria"],"affiliations":[{"raw_affiliation_string":"Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz, Austria","institution_ids":["https://openalex.org/I4210158379"]},{"raw_affiliation_string":"Johann Radon Inst. for Comput. & Appl. Math. (RICAM), Linz, Austria","institution_ids":["https://openalex.org/I4210158379"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5041230403"],"corresponding_institution_ids":["https://openalex.org/I2802519937","https://openalex.org/I4210112279"],"apc_list":null,"apc_paid":null,"fwci":12.1966,"has_fulltext":false,"cited_by_count":144,"citation_normalized_percentile":{"value":0.99171247,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"56","issue":"7","first_page":"3523","last_page":"3539"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"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":0.9995999932289124,"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/T10891","display_name":"Radar Systems and Signal Processing","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"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/matrix","display_name":"Matrix (chemical analysis)","score":0.44010990858078003},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4263598322868347},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.40806344151496887},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3913789391517639},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37970536947250366},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.264161080121994},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.07595780491828918}],"concepts":[{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.44010990858078003},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4263598322868347},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40806344151496887},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3913789391517639},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37970536947250366},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.264161080121994},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.07595780491828918},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tit.2010.2048466","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2010.2048466","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-00541297v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00541297","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":"IEEE Transactions on Information Theory, 2010, 56 (7), pp.3523--3539. &#x27E8;10.1109/TIT.2010.2048466&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:infoscience.tind.io:136769","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/136769","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"research article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00541297v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00541297","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":"IEEE Transactions on Information Theory, 2010, 56 (7), pp.3523--3539. &#x27E8;10.1109/TIT.2010.2048466&#x27E9;","raw_type":"Journal articles"},"sustainable_development_goals":[{"display_name":"Quality Education","score":0.5,"id":"https://metadata.un.org/sdg/4"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1492835675","https://openalex.org/W1537193711","https://openalex.org/W1592477457","https://openalex.org/W1984305442","https://openalex.org/W2008740515","https://openalex.org/W2020775053","https://openalex.org/W2021302824","https://openalex.org/W2028781966","https://openalex.org/W2050000141","https://openalex.org/W2099641086","https://openalex.org/W2099741732","https://openalex.org/W2116148865","https://openalex.org/W2119647652","https://openalex.org/W2127565671","https://openalex.org/W2135269774","https://openalex.org/W2136235822","https://openalex.org/W2142940228","https://openalex.org/W2145889472","https://openalex.org/W2147656689","https://openalex.org/W2151186643","https://openalex.org/W2154332973","https://openalex.org/W2155981690","https://openalex.org/W2156447271","https://openalex.org/W2157656280","https://openalex.org/W2160547390","https://openalex.org/W2161219071","https://openalex.org/W2164452299","https://openalex.org/W2170050981","https://openalex.org/W2547588342","https://openalex.org/W4247201904","https://openalex.org/W4285719527","https://openalex.org/W6684954309"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2350741829","https://openalex.org/W2530322880"],"abstract_inverted_index":{"This":[0],"paper":[1],"treats":[2],"the":[3,156,159,172,194,211],"problem":[4,24],"of":[5,59,123,198],"learning":[6],"a":[7,13,31,63,71,111,124,162,166,205],"dictionary":[8,67,112,160],"providing":[9],"sparse":[10,169],"representations":[11],"for":[12,138],"given":[14],"signal":[15,212],"class,":[16],"via":[17],"\u2113":[18,126],"<sub":[19,39,46,51,80,87,92,127],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[20,40,47,52,57,81,88,93,98,128],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sub>":[21,41,82,129],"-minimization.":[22],"The":[23,104,188],"can":[25,117],"also":[26],"be":[27,118],"seen":[28],"as":[29,120],"factorizing":[30],"d":[32,64],"\u00d7":[33,65,73],"N":[34,74,201,215],"matrix":[35,68,76],"Y":[36,133],"=":[37,78,134],"(y":[38],".":[42,43,44,83,84,85],"y":[45,50],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">N</sub>":[48,89],"),":[49,90],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</sub>":[53,94],"\u2208":[54,95],"\u211d":[55,96],"<sup":[56,97],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">d</sup>":[58],"training":[60,199],"signals":[61],"into":[62],"K":[66,72],"\u03a6":[69,135],"and":[70,141],"coefficient":[75,113,142,173],"X":[77],"(x":[79],"x":[86,91],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">K</sup>":[99],",":[100],"which":[101,151],"is":[102,109,161,176,192],"sparse.":[103],"exact":[105],"question":[106],"studied":[107],"here":[108],"when":[110,158],"pair":[114],"(\u03a6,":[115],"X)":[116],"recovered":[119],"local":[121,147],"minimum":[122],"(nonconvex)":[125],"-criterion":[130],"with":[131,185,210],"input":[132],"X.":[136],"First,":[137],"general":[139],"dictionaries":[140],"matrices,":[143],"algebraic":[144],"conditions":[145],"ensuring":[146],"identifiability":[148],"are":[149,152,182],"derived,":[150],"then":[153],"specialized":[154],"to":[155,204,222],"case":[157],"basis.":[163],"Finally,":[164],"assuming":[165],"random":[167],"Bernoulli-Gaussian":[168],"model":[170],"on":[171],"matrix,":[174],"it":[175],"shown":[177],"that":[178,193],"sufficiently":[179],"incoherent":[180],"bases":[181],"locally":[183],"identifiable":[184],"high":[186],"probability.":[187],"perhaps":[189],"surprising":[190],"result":[191],"typically":[195],"sufficient":[196],"number":[197],"samples":[200],"grows":[202],"up":[203],"logarithmic":[206],"factor":[207],"only":[208],"linearly":[209],"dimension,":[213],"i.e.,":[214],"\u2248":[216],"CK":[217],"log":[218],"K,":[219],"in":[220],"contrast":[221],"previous":[223],"approaches":[224],"requiring":[225],"combinatorially":[226],"many":[227],"samples.":[228]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":15},{"year":2015,"cited_by_count":12},{"year":2014,"cited_by_count":16},{"year":2013,"cited_by_count":15},{"year":2012,"cited_by_count":12}],"updated_date":"2026-02-27T16:54:17.756197","created_date":"2016-06-24T00:00:00"}
