{"id":"https://openalex.org/W1559813187","doi":"https://doi.org/10.1109/lsp.2015.2450505","title":"Regularization Paths for Re-Weighted Nuclear Norm Minimization","display_name":"Regularization Paths for Re-Weighted Nuclear Norm Minimization","publication_year":2015,"publication_date":"2015-07-07","ids":{"openalex":"https://openalex.org/W1559813187","doi":"https://doi.org/10.1109/lsp.2015.2450505","mag":"1559813187"},"language":"en","primary_location":{"id":"doi:10.1109/lsp.2015.2450505","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2015.2450505","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","raw_type":"journal-article"},"type":"article","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/A5058423196","display_name":"Niclas Blomberg","orcid":null},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Niclas Blomberg","raw_affiliation_strings":["Department of Automatic Control, KTH\u2013Royal Institute of Technology, Stockholm, Sweden","Department of Automatic Control and ACCESS Linnaeus Center, School of Electrical Engineering, KTH Royal Institute of Technology, Stockholm, Sweden"],"affiliations":[{"raw_affiliation_string":"Department of Automatic Control, KTH\u2013Royal Institute of Technology, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]},{"raw_affiliation_string":"Department of Automatic Control and ACCESS Linnaeus Center, School of Electrical Engineering, KTH Royal Institute of Technology, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057105677","display_name":"Cristian R. Rojas","orcid":"https://orcid.org/0000-0003-0355-2663"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Cristian R. Rojas","raw_affiliation_strings":["Department of Automatic Control, KTH\u2013Royal Institute of Technology, Stockholm, Sweden","Department of Automatic Control and ACCESS Linnaeus Center, School of Electrical Engineering, KTH Royal Institute of Technology, Stockholm, Sweden"],"affiliations":[{"raw_affiliation_string":"Department of Automatic Control, KTH\u2013Royal Institute of Technology, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]},{"raw_affiliation_string":"Department of Automatic Control and ACCESS Linnaeus Center, School of Electrical Engineering, KTH Royal Institute of Technology, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045354671","display_name":"Bo Wahlberg","orcid":"https://orcid.org/0000-0002-1927-1690"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Bo Wahlberg","raw_affiliation_strings":["Department of Automatic Control, KTH\u2013Royal Institute of Technology, Stockholm, Sweden","Department of Automatic Control and ACCESS Linnaeus Center, School of Electrical Engineering, KTH Royal Institute of Technology, Stockholm, Sweden"],"affiliations":[{"raw_affiliation_string":"Department of Automatic Control, KTH\u2013Royal Institute of Technology, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]},{"raw_affiliation_string":"Department of Automatic Control and ACCESS Linnaeus Center, School of Electrical Engineering, KTH Royal Institute of Technology, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5058423196"],"corresponding_institution_ids":["https://openalex.org/I86987016"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.02538616,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"22","issue":"11","first_page":"1980","last_page":"1984"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing 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/T10500","display_name":"Sparse and Compressive Sensing 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/T11038","display_name":"Advanced SAR Imaging Techniques","score":0.9969000220298767,"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"}},{"id":"https://openalex.org/T10534","display_name":"Structural Health Monitoring Techniques","score":0.9909999966621399,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/mathematical-optimization","display_name":"Mathematical optimization","score":0.6331998705863953},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5924782752990723},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5503491759300232},{"id":"https://openalex.org/keywords/regularization-perspectives-on-support-vector-machines","display_name":"Regularization perspectives on support vector machines","score":0.5043681859970093},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.48722854256629944},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4503999948501587},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4471750259399414},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4356180429458618},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38815703988075256},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3266136646270752},{"id":"https://openalex.org/keywords/tikhonov-regularization","display_name":"Tikhonov regularization","score":0.32418984174728394},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.31641507148742676},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.30661481618881226},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.1538344919681549},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12447541952133179}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6331998705863953},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5924782752990723},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5503491759300232},{"id":"https://openalex.org/C141718189","wikidata":"https://www.wikidata.org/wiki/Q7309628","display_name":"Regularization perspectives on support vector machines","level":4,"score":0.5043681859970093},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.48722854256629944},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4503999948501587},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4471750259399414},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4356180429458618},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38815703988075256},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3266136646270752},{"id":"https://openalex.org/C152442038","wikidata":"https://www.wikidata.org/wiki/Q2778212","display_name":"Tikhonov regularization","level":3,"score":0.32418984174728394},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31641507148742676},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.30661481618881226},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.1538344919681549},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12447541952133179},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/lsp.2015.2450505","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2015.2450505","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.75}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1505506151","https://openalex.org/W1534416612","https://openalex.org/W1868559974","https://openalex.org/W1916337001","https://openalex.org/W1966096622","https://openalex.org/W2029213856","https://openalex.org/W2042107404","https://openalex.org/W2056145308","https://openalex.org/W2060854861","https://openalex.org/W2065313971","https://openalex.org/W2074471762","https://openalex.org/W2109706083","https://openalex.org/W2118550318","https://openalex.org/W2119556711","https://openalex.org/W2145712233","https://openalex.org/W2145831204","https://openalex.org/W2161374719","https://openalex.org/W2218569681","https://openalex.org/W2296319761","https://openalex.org/W2963033846","https://openalex.org/W4249513058","https://openalex.org/W6681332534","https://openalex.org/W6681436789","https://openalex.org/W6688318578"],"related_works":["https://openalex.org/W2366023887","https://openalex.org/W2388364587","https://openalex.org/W2935233291","https://openalex.org/W2062975788","https://openalex.org/W2385735574","https://openalex.org/W2030398504","https://openalex.org/W2050033254","https://openalex.org/W2075210326","https://openalex.org/W2127000180","https://openalex.org/W2062342781"],"abstract_inverted_index":{"We":[0],"consider":[1],"a":[2,29,41,46,51,70,93,98,117,135],"class":[3],"of":[4,54,100,120,122],"weighted":[5,136],"nuclear":[6,23,47],"norm":[7,24,48],"optimization":[8,114],"problems":[9],"with":[10,126],"important":[11],"applications":[12],"in":[13],"signal":[14],"processing,":[15],"system":[16],"identification,":[17],"and":[18,64],"model":[19,139],"order":[20,140],"reduction.":[21],"The":[22,73,104,130],"is":[25,38,67,76,87,106,132],"commonly":[26],"used":[27],"as":[28,97],"convex":[30],"heuristic":[31],"for":[32,116],"matrix":[33,138],"rank":[34],"constraints.":[35],"Our":[36],"objective":[37],"to":[39,45,79,92,111],"minimize":[40],"quadratic":[42],"cost":[43],"subject":[44],"constraint":[49,66],"on":[50,134],"linear":[52],"function":[53,99],"the":[55,59,62,65,81,88,101,113,123],"decision":[56],"variables,":[57],"where":[58],"trade-off":[60],"between":[61],"fit":[63],"governed":[68],"by":[69],"regularization":[71,84,102,124],"parameter.":[72,103],"main":[74],"contribution":[75],"an":[77],"algorithm":[78,131],"determine":[80],"so-called":[82],"approximate":[83],"path,":[85],"which":[86],"optimal":[89],"solution":[90],"up":[91],"given":[94],"error":[95,128],"tolerance":[96],"advantage":[105],"that":[107],"we":[108],"only":[109],"have":[110],"solve":[112],"problem":[115],"fixed":[118],"number":[119],"values":[121],"parameter,":[125],"guaranteed":[127],"tolerance.":[129],"exemplified":[133],"Hankel":[137],"reduction":[141],"problem.":[142]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}