{"id":"https://openalex.org/W4225740441","doi":"https://doi.org/10.1109/lcsys.2022.3166640","title":"<i>H</i> <sup>2</sup>-Optimal Reduction of Positive Networks Using Riemannian Augmented Lagrangian Method","display_name":"<i>H</i> <sup>2</sup>-Optimal Reduction of Positive Networks Using Riemannian Augmented Lagrangian Method","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4225740441","doi":"https://doi.org/10.1109/lcsys.2022.3166640"},"language":"en","primary_location":{"id":"doi:10.1109/lcsys.2022.3166640","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lcsys.2022.3166640","pdf_url":null,"source":{"id":"https://openalex.org/S4306422535","display_name":"IEEE Control Systems Letters","issn_l":"2475-1456","issn":["2475-1456"],"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 Control Systems 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/A5011135622","display_name":"Sota Misawa","orcid":"https://orcid.org/0000-0002-2169-5994"},"institutions":[{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Sota Misawa","raw_affiliation_strings":["Graduate School of Information Science and Technology, The University of Tokyo, Tokyo, Japan"],"raw_orcid":"https://orcid.org/0000-0002-2169-5994","affiliations":[{"raw_affiliation_string":"Graduate School of Information Science and Technology, The University of Tokyo, Tokyo, Japan","institution_ids":["https://openalex.org/I74801974"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091598191","display_name":"Kazuhiro Sato","orcid":"https://orcid.org/0000-0003-1895-6548"},"institutions":[{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kazuhiro Sato","raw_affiliation_strings":["Graduate School of Information Science and Technology, The University of Tokyo, Tokyo, Japan"],"raw_orcid":"https://orcid.org/0000-0003-1895-6548","affiliations":[{"raw_affiliation_string":"Graduate School of Information Science and Technology, The University of Tokyo, Tokyo, Japan","institution_ids":["https://openalex.org/I74801974"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5011135622"],"corresponding_institution_ids":["https://openalex.org/I74801974"],"apc_list":null,"apc_paid":null,"fwci":0.2504,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.49013039,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"6","issue":null,"first_page":"2539","last_page":"2544"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9564999938011169,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10857","display_name":"Advanced Electron Microscopy Techniques and Applications","score":0.9542999863624573,"subfield":{"id":"https://openalex.org/subfields/1315","display_name":"Structural Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.6206748485565186},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6116524934768677},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.6074480414390564},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.5774567127227783},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5380020141601562},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.45580434799194336},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.44616031646728516},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4243197441101074},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.4145479202270508},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39041954278945923},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3478918671607971},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28208357095718384},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.19786444306373596},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1539231240749359},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.09862267971038818},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08585000038146973}],"concepts":[{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.6206748485565186},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6116524934768677},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.6074480414390564},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.5774567127227783},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5380020141601562},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.45580434799194336},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.44616031646728516},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4243197441101074},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.4145479202270508},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39041954278945923},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3478918671607971},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28208357095718384},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.19786444306373596},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1539231240749359},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.09862267971038818},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08585000038146973},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/lcsys.2022.3166640","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lcsys.2022.3166640","pdf_url":null,"source":{"id":"https://openalex.org/S4306422535","display_name":"IEEE Control Systems Letters","issn_l":"2475-1456","issn":["2475-1456"],"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 Control Systems Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2798678606","display_name":null,"funder_award_id":"20K14760","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W615876487","https://openalex.org/W1783235837","https://openalex.org/W1891861977","https://openalex.org/W1966992674","https://openalex.org/W2011053055","https://openalex.org/W2017999133","https://openalex.org/W2064733273","https://openalex.org/W2094014274","https://openalex.org/W2136195193","https://openalex.org/W2141770513","https://openalex.org/W2141807041","https://openalex.org/W2150915639","https://openalex.org/W2152896489","https://openalex.org/W2188751308","https://openalex.org/W2271974951","https://openalex.org/W2734643148","https://openalex.org/W2753939719","https://openalex.org/W2796074318","https://openalex.org/W2799024262","https://openalex.org/W2894212516","https://openalex.org/W2963081525","https://openalex.org/W2963704853","https://openalex.org/W2968374706","https://openalex.org/W3097532239","https://openalex.org/W3104705084","https://openalex.org/W3104834496","https://openalex.org/W4205293427","https://openalex.org/W4212889321","https://openalex.org/W4213232118","https://openalex.org/W4323539420"],"related_works":["https://openalex.org/W4311922918","https://openalex.org/W4307320415","https://openalex.org/W2098162112","https://openalex.org/W1513235864","https://openalex.org/W2952130664","https://openalex.org/W2524653688","https://openalex.org/W4306663322","https://openalex.org/W4315473876","https://openalex.org/W2314120527","https://openalex.org/W2090965439"],"abstract_inverted_index":{"In":[0],"this":[1],"letter,":[2],"we":[3,123],"formulate":[4],"the":[5,23,34,42,46,53,66,69,73,77,84,87,92,102,110,114,118,132,136],"model":[6,58],"reduction":[7,43,59],"problem":[8,21],"of":[9,33,45,52,60,68,86,94,113,120,138],"a":[10,17,125],"stable":[11],"and":[12,36,97,108,128,146],"positive":[13,61],"network":[14,38,62,88],"system":[15,89],"as":[16,72],"constrained":[18],"Riemannian":[19,103,111],"optimization":[20],"with":[22,131],"<inline-formula":[24,139,147],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[25,140,148],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[26,141,149],"<tex-math":[27,142,150],"notation=\"LaTeX\">$H^{2}$":[28,143],"</tex-math></inline-formula>":[29,144,153],"-error":[30,145],"objective":[31],"function":[32],"original":[35],"reduced":[37],"systems.":[39],"We":[40],"improve":[41],"performance":[44],"clustering-based":[47,70,133],"method,":[48,122],"which":[49],"is":[50],"one":[51],"most":[54],"known":[55],"methods":[56],"for":[57,76],"systems,":[63],"by":[64,100],"using":[65],"output":[67],"method":[71,82,106,134],"initial":[74],"point":[75],"proposed":[78,81],"method.":[79],"The":[80],"reduces":[83],"dimension":[85],"while":[90],"preserving":[91],"properties":[93],"stability,":[95],"positivity,":[96],"interconnection":[98],"structure":[99],"applying":[101],"augmented":[104],"Lagrangian":[105],"(RALM)":[107],"deriving":[109],"gradient":[112],"Lagrangian.":[115],"To":[116],"check":[117],"efficiency":[119],"our":[121],"conduct":[124],"numerical":[126],"experiment":[127],"compare":[129],"it":[130],"in":[135],"sense":[137],"notation=\"LaTeX\">$H^{\\infty":[151],"}$":[152],"-error.":[154]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}