{"id":"https://openalex.org/W3083035255","doi":"https://doi.org/10.1109/tsp.2020.3021247","title":"Online Proximal Learning Over Jointly Sparse Multitask Networks With $\\ell _{\\infty, 1}$ Regularization","display_name":"Online Proximal Learning Over Jointly Sparse Multitask Networks With $\\ell _{\\infty, 1}$ Regularization","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3083035255","doi":"https://doi.org/10.1109/tsp.2020.3021247","mag":"3083035255"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2020.3021247","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2020.3021247","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-03347269","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082577449","display_name":"Danqi Jin","orcid":"https://orcid.org/0000-0001-9435-2231"},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]},{"id":"https://openalex.org/I890469752","display_name":"Ministry of Industry and Information Technology","ror":"https://ror.org/0385nmy68","country_code":"CN","type":"government","lineage":["https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Danqi Jin","raw_affiliation_strings":["Centre of Intelligent Acoustics and Immersive Communications, School of Marine Science and Technology, Northwestern Polytechinical University, Xi\u2019an, China","Key Laboratory of Ocean Acoustics and Sensing, Ministry of Industry and Information Technology, Xi\u2019an, China","Centre of Intelligent Acoustics and Immersive Communications, School of Marine Science and Technology, Northwestern Polytechinical University, Xi'an, China","Key Laboratory of Ocean Acoustics and Sensing, Ministry of Industry and Information Technology, Xi'an, China"],"affiliations":[{"raw_affiliation_string":"Centre of Intelligent Acoustics and Immersive Communications, School of Marine Science and Technology, Northwestern Polytechinical University, Xi\u2019an, China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"Key Laboratory of Ocean Acoustics and Sensing, Ministry of Industry and Information Technology, Xi\u2019an, China","institution_ids":["https://openalex.org/I890469752"]},{"raw_affiliation_string":"Centre of Intelligent Acoustics and Immersive Communications, School of Marine Science and Technology, Northwestern Polytechinical University, Xi'an, China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"Key Laboratory of Ocean Acoustics and Sensing, Ministry of Industry and Information Technology, Xi'an, China","institution_ids":["https://openalex.org/I890469752"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100333004","display_name":"Jie Chen","orcid":"https://orcid.org/0000-0003-2306-8860"},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]},{"id":"https://openalex.org/I890469752","display_name":"Ministry of Industry and Information Technology","ror":"https://ror.org/0385nmy68","country_code":"CN","type":"government","lineage":["https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jie Chen","raw_affiliation_strings":["Centre of Intelligent Acoustics and Immersive Communications, School of Marine Science and Technology, Northwestern Polytechinical University, Xi\u2019an, China","Key Laboratory of Ocean Acoustics and Sensing, Ministry of Industry and Information Technology, Xi\u2019an, China","Centre of Intelligent Acoustics and Immersive Communications, School of Marine Science and Technology, Northwestern Polytechinical University, Xi'an, China","Key Laboratory of Ocean Acoustics and Sensing, Ministry of Industry and Information Technology, Xi'an, China"],"affiliations":[{"raw_affiliation_string":"Centre of Intelligent Acoustics and Immersive Communications, School of Marine Science and Technology, Northwestern Polytechinical University, Xi\u2019an, China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"Key Laboratory of Ocean Acoustics and Sensing, Ministry of Industry and Information Technology, Xi\u2019an, China","institution_ids":["https://openalex.org/I890469752"]},{"raw_affiliation_string":"Centre of Intelligent Acoustics and Immersive Communications, School of Marine Science and Technology, Northwestern Polytechinical University, Xi'an, China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"Key Laboratory of Ocean Acoustics and Sensing, Ministry of Industry and Information Technology, Xi'an, China","institution_ids":["https://openalex.org/I890469752"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009808175","display_name":"C\u00e9dric Richard","orcid":"https://orcid.org/0000-0003-2890-141X"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I201841394","display_name":"Universit\u00e9 C\u00f4te d'Azur","ror":"https://ror.org/019tgvf94","country_code":"FR","type":"education","lineage":["https://openalex.org/I201841394"]},{"id":"https://openalex.org/I4210126779","display_name":"Observatoire de la C\u00f4te d\u2019Azur","ror":"https://ror.org/039fj2469","country_code":"FR","type":"facility","lineage":["https://openalex.org/I201841394","https://openalex.org/I4210126779"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Cedric Richard","raw_affiliation_strings":["CNRS, Universit\u00e9 C\u00f4te d\u2019Azur, Nice, France","CNRS, Universit\u00e9 C\u00f4te d'Azur, Nice, France"],"affiliations":[{"raw_affiliation_string":"CNRS, Universit\u00e9 C\u00f4te d\u2019Azur, Nice, France","institution_ids":["https://openalex.org/I4210126779","https://openalex.org/I201841394","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"CNRS, Universit\u00e9 C\u00f4te d'Azur, Nice, France","institution_ids":["https://openalex.org/I4210126779","https://openalex.org/I201841394","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056129529","display_name":"Jingdong Chen","orcid":"https://orcid.org/0000-0003-0083-9247"},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]},{"id":"https://openalex.org/I890469752","display_name":"Ministry of Industry and Information Technology","ror":"https://ror.org/0385nmy68","country_code":"CN","type":"government","lineage":["https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jingdong Chen","raw_affiliation_strings":["Centre of Intelligent Acoustics and Immersive Communications, School of Marine Science and Technology, Northwestern Polytechinical University, Xi\u2019an, China","Key Laboratory of Ocean Acoustics and Sensing, Ministry of Industry and Information Technology, Xi\u2019an, China","Key Laboratory of Ocean Acoustics and Sensing, Ministry of Industry and Information Technology, Xi'an, China","Centre of Intelligent Acoustics and Immersive Communications, School of Marine Science and Technology, Northwestern Polytechinical University, Xi'an, China"],"affiliations":[{"raw_affiliation_string":"Centre of Intelligent Acoustics and Immersive Communications, School of Marine Science and Technology, Northwestern Polytechinical University, Xi\u2019an, China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"Key Laboratory of Ocean Acoustics and Sensing, Ministry of Industry and Information Technology, Xi\u2019an, China","institution_ids":["https://openalex.org/I890469752"]},{"raw_affiliation_string":"Key Laboratory of Ocean Acoustics and Sensing, Ministry of Industry and Information Technology, Xi'an, China","institution_ids":["https://openalex.org/I890469752"]},{"raw_affiliation_string":"Centre of Intelligent Acoustics and Immersive Communications, School of Marine Science and Technology, Northwestern Polytechinical University, Xi'an, China","institution_ids":["https://openalex.org/I17145004"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5082577449"],"corresponding_institution_ids":["https://openalex.org/I17145004","https://openalex.org/I890469752"],"apc_list":null,"apc_paid":null,"fwci":0.8973,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.7001561,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"68","issue":null,"first_page":"6319","last_page":"6335"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":0.9998999834060669,"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/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":0.9998999834060669,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9987000226974487,"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/T10860","display_name":"Speech and Audio Processing","score":0.9987000226974487,"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/regularization","display_name":"Regularization (linguistics)","score":0.6457290649414062},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5745854377746582},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5273795127868652},{"id":"https://openalex.org/keywords/multi-task-learning","display_name":"Multi-task learning","score":0.47505947947502136},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.4328418970108032},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41666871309280396},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3687759041786194},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3311294913291931},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2938264012336731}],"concepts":[{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.6457290649414062},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5745854377746582},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5273795127868652},{"id":"https://openalex.org/C28006648","wikidata":"https://www.wikidata.org/wiki/Q6934509","display_name":"Multi-task learning","level":3,"score":0.47505947947502136},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.4328418970108032},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41666871309280396},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3687759041786194},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3311294913291931},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2938264012336731},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","level":1,"score":0.0},{"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},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tsp.2020.3021247","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2020.3021247","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-03347269v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03347269","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 Signal Processing, 2020, 68, pp.6319-6335. &#x27E8;10.1109/TSP.2020.3021247&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-03347269v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03347269","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 Signal Processing, 2020, 68, pp.6319-6335. &#x27E8;10.1109/TSP.2020.3021247&#x27E9;","raw_type":"Journal articles"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3909335432","display_name":null,"funder_award_id":"61831019","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7520581741","display_name":null,"funder_award_id":"B18041","funder_id":"https://openalex.org/F4320327912","funder_display_name":"Higher Education Discipline Innovation Project"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321392","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86"},{"id":"https://openalex.org/F4320327912","display_name":"Higher Education Discipline Innovation Project","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":60,"referenced_works":["https://openalex.org/W338925043","https://openalex.org/W1480312878","https://openalex.org/W1546590558","https://openalex.org/W1551912413","https://openalex.org/W1587744656","https://openalex.org/W1986302543","https://openalex.org/W2012445782","https://openalex.org/W2017856064","https://openalex.org/W2024307985","https://openalex.org/W2025755239","https://openalex.org/W2031607104","https://openalex.org/W2046793177","https://openalex.org/W2047923615","https://openalex.org/W2057491164","https://openalex.org/W2071607622","https://openalex.org/W2073750241","https://openalex.org/W2074054045","https://openalex.org/W2077964948","https://openalex.org/W2092734317","https://openalex.org/W2093795816","https://openalex.org/W2098743149","https://openalex.org/W2103644547","https://openalex.org/W2106398669","https://openalex.org/W2106407813","https://openalex.org/W2107806930","https://openalex.org/W2107861471","https://openalex.org/W2108924122","https://openalex.org/W2115806236","https://openalex.org/W2118776392","https://openalex.org/W2119293025","https://openalex.org/W2119434824","https://openalex.org/W2129927143","https://openalex.org/W2134438999","https://openalex.org/W2144616873","https://openalex.org/W2145688801","https://openalex.org/W2149414429","https://openalex.org/W2295500362","https://openalex.org/W2400337965","https://openalex.org/W2530728613","https://openalex.org/W2551543312","https://openalex.org/W2589814220","https://openalex.org/W2782574184","https://openalex.org/W2809216150","https://openalex.org/W2885660987","https://openalex.org/W2896675734","https://openalex.org/W2913535645","https://openalex.org/W2921557659","https://openalex.org/W2942979385","https://openalex.org/W2962907301","https://openalex.org/W2963157432","https://openalex.org/W2963529998","https://openalex.org/W2997993128","https://openalex.org/W3007376870","https://openalex.org/W3014507393","https://openalex.org/W4229583111","https://openalex.org/W4238850922","https://openalex.org/W4239240501","https://openalex.org/W4244393449","https://openalex.org/W6674988045","https://openalex.org/W6675873461"],"related_works":["https://openalex.org/W2009525028","https://openalex.org/W4321064619","https://openalex.org/W2053599029","https://openalex.org/W3011179836","https://openalex.org/W2962925412","https://openalex.org/W2023672523","https://openalex.org/W4246719751","https://openalex.org/W2483165346","https://openalex.org/W4297752497","https://openalex.org/W2010597174"],"abstract_inverted_index":{"Modeling":[0],"relations":[1],"between":[2],"local":[3,36],"optimum":[4],"parameter":[5],"vectors":[6],"to":[7,50,76,103,123,138],"estimate":[8],"in":[9,56,128],"multitask":[10,112],"networks":[11],"has":[12],"attracted":[13],"much":[14],"attention":[15],"over":[16],"the":[17,35,39,52,57,62,105,125,129,145,148],"last":[18],"years.":[19],"This":[20],"work":[21],"considers":[22],"a":[23,85,99,110],"distributed":[24],"optimization":[25],"problem":[26],"with":[27],"jointly":[28,53],"sparse":[29,41,54],"structure":[30,55],"among":[31],"nodes,":[32],"that":[33],"is,":[34],"solutions":[37],"have":[38,47],"same":[40],"support":[42],"set.":[43],"Several":[44],"mixed":[45],"norm":[46],"been":[48],"proposed":[49],"address":[51],"literature.":[58],"Among":[59],"several":[60],"candidates,":[61],"(reweighted)":[63,86],"\u2113":[64,87],"<sub":[65,88],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[66,89],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u221e,1</sub>":[67,90],"-norm":[68,91],"is":[69,73],"element-wise":[70],"separable,":[71],"it":[72],"more":[74],"convenient":[75],"evaluate":[77],"their":[78],"approximate":[79],"proximal":[80,100,111],"operators.":[81],"Thus":[82],"by":[83],"introducing":[84],"penalty":[92],"term":[93],"at":[94],"each":[95],"node,":[96],"and":[97,131],"using":[98],"gradient":[101],"method":[102],"minimize":[104],"regularized":[106],"cost,":[107],"we":[108],"devise":[109],"diffusion":[113],"LMS":[114],"algorithm":[115,126],"which":[116],"can":[117],"promote":[118],"joint-sparsity.":[119],"Analyses":[120],"are":[121,136],"provided":[122],"characterize":[124],"behavior":[127],"mean":[130],"mean-square":[132],"sense.":[133],"Simulation":[134],"results":[135],"presented":[137],"show":[139],"its":[140],"effectiveness,":[141],"as":[142,144],"well":[143],"accuracy":[146],"of":[147],"theoretical":[149],"findings.":[150]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":5},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}