{"id":"https://openalex.org/W3004184337","doi":"https://doi.org/10.1109/tsp.2020.2970336","title":"Adaptation and Learning Over Networks Under Subspace Constraints\u2014Part I: Stability Analysis","display_name":"Adaptation and Learning Over Networks Under Subspace Constraints\u2014Part I: Stability Analysis","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3004184337","doi":"https://doi.org/10.1109/tsp.2020.2970336","mag":"3004184337"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2020.2970336","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2020.2970336","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1905.08750","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015999129","display_name":"Roula Nassif","orcid":"https://orcid.org/0000-0001-9663-8559"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]},{"id":"https://openalex.org/I98635879","display_name":"American University of Beirut","ror":"https://ror.org/04pznsd21","country_code":"LB","type":"education","lineage":["https://openalex.org/I98635879"]}],"countries":["CH","LB"],"is_corresponding":false,"raw_author_name":"Roula Nassif","raw_affiliation_strings":["American University of Beirut, Riad El-Solh, Beirut, Lebanon","\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland"],"raw_orcid":"https://orcid.org/0000-0001-9663-8559","affiliations":[{"raw_affiliation_string":"American University of Beirut, Riad El-Solh, Beirut, Lebanon","institution_ids":["https://openalex.org/I98635879"]},{"raw_affiliation_string":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083805703","display_name":"Stefan Vlaski","orcid":"https://orcid.org/0000-0002-0616-3076"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Stefan Vlaski","raw_affiliation_strings":["Institute of Electrical Engineering, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland"],"raw_orcid":"https://orcid.org/0000-0002-0616-3076","affiliations":[{"raw_affiliation_string":"Institute of Electrical Engineering, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091103447","display_name":"Ali H. Sayed","orcid":"https://orcid.org/0000-0002-5125-5519"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Ali H. Sayed","raw_affiliation_strings":["Institute of Electrical Engineering, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland"],"raw_orcid":"https://orcid.org/0000-0002-5125-5519","affiliations":[{"raw_affiliation_string":"Institute of Electrical Engineering, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.8165,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.9042189,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"68","issue":null,"first_page":"1346","last_page":"1360"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.9861999750137329,"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/subspace-topology","display_name":"Subspace topology","score":0.7669537663459778},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6503386497497559},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.6156532764434814},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.611734926700592},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6098902225494385},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5943064093589783},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.5766316056251526},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5687007308006287},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.5651810765266418},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.4483456015586853},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.43289482593536377},{"id":"https://openalex.org/keywords/adaptation","display_name":"Adaptation (eye)","score":0.4322948455810547},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33153006434440613},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.27217209339141846},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.26908940076828003},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13484200835227966},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.1031997799873352}],"concepts":[{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.7669537663459778},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6503386497497559},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.6156532764434814},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.611734926700592},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6098902225494385},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5943064093589783},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.5766316056251526},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5687007308006287},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.5651810765266418},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4483456015586853},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.43289482593536377},{"id":"https://openalex.org/C139807058","wikidata":"https://www.wikidata.org/wiki/Q352374","display_name":"Adaptation (eye)","level":2,"score":0.4322948455810547},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33153006434440613},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.27217209339141846},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.26908940076828003},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13484200835227966},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.1031997799873352},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tsp.2020.2970336","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2020.2970336","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:arXiv.org:1905.08750","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1905.08750","pdf_url":"https://arxiv.org/pdf/1905.08750","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:infoscience.epfl.ch:277302","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/277302","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":"WoS","raw_type":"research article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1905.08750","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1905.08750","pdf_url":"https://arxiv.org/pdf/1905.08750","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":61,"referenced_works":["https://openalex.org/W653761051","https://openalex.org/W1568288633","https://openalex.org/W1578099820","https://openalex.org/W1968191600","https://openalex.org/W1970997001","https://openalex.org/W1983933235","https://openalex.org/W1998209214","https://openalex.org/W2004445469","https://openalex.org/W2012445782","https://openalex.org/W2025184650","https://openalex.org/W2042664989","https://openalex.org/W2044212084","https://openalex.org/W2052279775","https://openalex.org/W2057325524","https://openalex.org/W2063434864","https://openalex.org/W2065633516","https://openalex.org/W2074796812","https://openalex.org/W2074878962","https://openalex.org/W2081178476","https://openalex.org/W2084361947","https://openalex.org/W2095578515","https://openalex.org/W2120286056","https://openalex.org/W2122293353","https://openalex.org/W2129906637","https://openalex.org/W2134400959","https://openalex.org/W2143862148","https://openalex.org/W2144244295","https://openalex.org/W2169818402","https://openalex.org/W2195972617","https://openalex.org/W2295500362","https://openalex.org/W2296319761","https://openalex.org/W2395868845","https://openalex.org/W2405727896","https://openalex.org/W2530728613","https://openalex.org/W2538000501","https://openalex.org/W2592211823","https://openalex.org/W2610857016","https://openalex.org/W2777336446","https://openalex.org/W2778725237","https://openalex.org/W2786777656","https://openalex.org/W2789890080","https://openalex.org/W2792298817","https://openalex.org/W2808733326","https://openalex.org/W2885209016","https://openalex.org/W2905915262","https://openalex.org/W2911868526","https://openalex.org/W2913535645","https://openalex.org/W2936912184","https://openalex.org/W2938504156","https://openalex.org/W2939925216","https://openalex.org/W2962907301","https://openalex.org/W2963395095","https://openalex.org/W2964067433","https://openalex.org/W2964075583","https://openalex.org/W3017195594","https://openalex.org/W3103253084","https://openalex.org/W3104550706","https://openalex.org/W3122968066","https://openalex.org/W4205987271","https://openalex.org/W4238850922","https://openalex.org/W4254313632"],"related_works":["https://openalex.org/W2896134808","https://openalex.org/W3172436493","https://openalex.org/W2957492749","https://openalex.org/W1887135636","https://openalex.org/W4287164812","https://openalex.org/W2386063599","https://openalex.org/W1975884855","https://openalex.org/W3213150849","https://openalex.org/W4285605394","https://openalex.org/W2025894073"],"abstract_inverted_index":{"This":[0,36],"paper":[1],"considers":[2],"optimization":[3,41],"problems":[4],"over":[5],"networks":[6],"where":[7],"agents":[8],"have":[9],"individual":[10,15],"objectives":[11,27],"to":[12,18,21,31,119],"meet,":[13],"or":[14],"parameter":[16],"vectors":[17],"estimate,":[19],"subject":[20],"subspace":[22,161],"constraints":[23],"that":[24,172],"require":[25],"the":[26,29,67,75,86,94,106,113,124,131,144,152,155,164,174,178,182,186],"across":[28],"network":[30,165],"lie":[32],"in":[33,91,101,130,173],"low-dimensional":[34],"subspaces.":[35],"constrained":[37],"formulation":[38],"includes":[39],"consensus":[40],"as":[42,55],"a":[43],"special":[44],"case,":[45],"and":[46,82,139,160],"allows":[47],"for":[48,109],"more":[49],"general":[50],"task":[51],"relatedness":[52],"models":[53],"such":[54,58],"smoothness.":[56],"While":[57],"formulations":[59],"can":[60],"be":[61],"solved":[62],"via":[63],"projected":[64],"gradient":[65,96,156],"descent,":[66],"resulting":[68],"algorithm":[69,184],"is":[70],"not":[71],"distributed.":[72],"Starting":[73],"from":[74],"centralized":[76,187],"solution,":[77],"we":[78],"propose":[79],"an":[80],"iterative":[81],"distributed":[83,115,183],"implementation":[84],"of":[85,105,126,154],"projection":[87],"step,":[88],"which":[89],"runs":[90],"parallel":[92],"with":[93],"stochastic":[95],"descent":[97],"update.":[98],"We":[99,128],"establish":[100],"this":[102],"Part":[103,133],"I":[104],"work":[107],"that,":[108],"small":[110,120,175],"step-sizes":[111],"\u03bc,":[112],"proposed":[114],"adaptive":[116],"strategy":[117],"leads":[118],"estimation":[121],"errors":[122],"on":[123,163],"order":[125],"\u03bc.":[127],"examine":[129],"accompanying":[132],"II":[134],"(R.":[135],"Nassif,":[136],"S.":[137],"Vlaski,":[138],"A.":[140],"H.":[141],"Sayed,":[142],"2019)":[143],"steady-state":[145,188],"performance.":[146,166,189],"The":[147,167],"results":[148,168],"will":[149,169],"reveal":[150],"explicitly":[151],"influence":[153],"noise,":[157],"data":[158],"characteristics,":[159],"constraints,":[162],"also":[170],"show":[171],"step-size":[176],"regime,":[177],"iterates":[179],"generated":[180],"by":[181],"achieve":[185]},"counts_by_year":[{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":7}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}
