{"id":"https://openalex.org/W3136613237","doi":"https://doi.org/10.1134/s0005117921030097","title":"Entropy-Randomized Projection","display_name":"Entropy-Randomized Projection","publication_year":2021,"publication_date":"2021-03-01","ids":{"openalex":"https://openalex.org/W3136613237","doi":"https://doi.org/10.1134/s0005117921030097","mag":"3136613237"},"language":"en","primary_location":{"id":"doi:10.1134/s0005117921030097","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0005117921030097","pdf_url":null,"source":{"id":"https://openalex.org/S134188425","display_name":"Automation and Remote Control","issn_l":"0005-1179","issn":["0005-1179","1608-3032"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Automation and Remote Control","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/A5113566225","display_name":"Yu. S. Popkov","orcid":null},"institutions":[{"id":"https://openalex.org/I1313323035","display_name":"Russian Academy of Sciences","ror":"https://ror.org/05qrfxd25","country_code":"RU","type":"funder","lineage":["https://openalex.org/I1313323035"]},{"id":"https://openalex.org/I4210157430","display_name":"V. A. Trapeznikov Institute of Control Sciences","ror":"https://ror.org/05f3yt521","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210157430","https://openalex.org/I4210164537"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Yu. S. Popkov","raw_affiliation_strings":["Federal Research Center \u201cComputer Science and Control,\u201d\nRussian Academy of Sciences, Moscow, 119333, Russia","Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, 117997, Russia"],"affiliations":[{"raw_affiliation_string":"Federal Research Center \u201cComputer Science and Control,\u201d\nRussian Academy of Sciences, Moscow, 119333, Russia","institution_ids":["https://openalex.org/I1313323035"]},{"raw_affiliation_string":"Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, 117997, Russia","institution_ids":["https://openalex.org/I4210157430"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029681629","display_name":"Yuri A. Dubnov","orcid":null},"institutions":[{"id":"https://openalex.org/I1313323035","display_name":"Russian Academy of Sciences","ror":"https://ror.org/05qrfxd25","country_code":"RU","type":"funder","lineage":["https://openalex.org/I1313323035"]},{"id":"https://openalex.org/I118501908","display_name":"National Research University Higher School of Economics","ror":"https://ror.org/055f7t516","country_code":"RU","type":"education","lineage":["https://openalex.org/I118501908"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Yu. A. Dubnov","raw_affiliation_strings":["Federal Research Center \u201cComputer Science and Control,\u201d\nRussian Academy of Sciences, Moscow, 119333, Russia","National Research University Higher School of Economics, Moscow, 101000, Russia"],"affiliations":[{"raw_affiliation_string":"Federal Research Center \u201cComputer Science and Control,\u201d\nRussian Academy of Sciences, Moscow, 119333, Russia","institution_ids":["https://openalex.org/I1313323035"]},{"raw_affiliation_string":"National Research University Higher School of Economics, Moscow, 101000, Russia","institution_ids":["https://openalex.org/I118501908"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034623562","display_name":"A. Yu. Popkov","orcid":"https://orcid.org/0000-0003-4039-7746"},"institutions":[{"id":"https://openalex.org/I1313323035","display_name":"Russian Academy of Sciences","ror":"https://ror.org/05qrfxd25","country_code":"RU","type":"funder","lineage":["https://openalex.org/I1313323035"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"A. Yu. Popkov","raw_affiliation_strings":["Federal Research Center \u201cComputer Science and Control,\u201d\nRussian Academy of Sciences, Moscow, 119333, Russia"],"affiliations":[{"raw_affiliation_string":"Federal Research Center \u201cComputer Science and Control,\u201d\nRussian Academy of Sciences, Moscow, 119333, Russia","institution_ids":["https://openalex.org/I1313323035"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5034623562","https://openalex.org/A5113566225"],"corresponding_institution_ids":["https://openalex.org/I1313323035","https://openalex.org/I4210157430"],"apc_list":null,"apc_paid":null,"fwci":0.3284,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.46242728,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"82","issue":"3","first_page":"490","last_page":"505"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.9904999732971191,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.9904999732971191,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9871000051498413,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10136","display_name":"Statistical Methods and Inference","score":0.9843000173568726,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7219071388244629},{"id":"https://openalex.org/keywords/entropy-maximization","display_name":"Entropy maximization","score":0.6737331748008728},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.6126177310943604},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5744157433509827},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5684630870819092},{"id":"https://openalex.org/keywords/projection-method","display_name":"Projection method","score":0.47264236211776733},{"id":"https://openalex.org/keywords/conditional-entropy","display_name":"Conditional entropy","score":0.4525063931941986},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4513295888900757},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.44150370359420776},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.42748332023620605},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.42390793561935425},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.393297404050827},{"id":"https://openalex.org/keywords/dykstras-projection-algorithm","display_name":"Dykstra's projection algorithm","score":0.3845834732055664},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.295405775308609},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2173980176448822},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.14175552129745483}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7219071388244629},{"id":"https://openalex.org/C127233936","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Entropy maximization","level":3,"score":0.6737331748008728},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.6126177310943604},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5744157433509827},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5684630870819092},{"id":"https://openalex.org/C65557600","wikidata":"https://www.wikidata.org/wiki/Q7249451","display_name":"Projection method","level":3,"score":0.47264236211776733},{"id":"https://openalex.org/C101721835","wikidata":"https://www.wikidata.org/wiki/Q813908","display_name":"Conditional entropy","level":3,"score":0.4525063931941986},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4513295888900757},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.44150370359420776},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.42748332023620605},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.42390793561935425},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.393297404050827},{"id":"https://openalex.org/C202426404","wikidata":"https://www.wikidata.org/wiki/Q5318686","display_name":"Dykstra's projection algorithm","level":2,"score":0.3845834732055664},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.295405775308609},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2173980176448822},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.14175552129745483},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1134/s0005117921030097","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0005117921030097","pdf_url":null,"source":{"id":"https://openalex.org/S134188425","display_name":"Automation and Remote Control","issn_l":"0005-1179","issn":["0005-1179","1608-3032"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Automation and Remote Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W11802270","https://openalex.org/W1554944419","https://openalex.org/W1571401318","https://openalex.org/W1577871831","https://openalex.org/W1755563775","https://openalex.org/W1976709621","https://openalex.org/W1987888496","https://openalex.org/W2001619934","https://openalex.org/W2019557834","https://openalex.org/W2040884411","https://openalex.org/W2053171205","https://openalex.org/W2072184377","https://openalex.org/W2075023573","https://openalex.org/W2099111195","https://openalex.org/W2117897510","https://openalex.org/W2129476886","https://openalex.org/W2133010742","https://openalex.org/W2147152072","https://openalex.org/W2153803020","https://openalex.org/W2154053567","https://openalex.org/W2160222246","https://openalex.org/W2171033594","https://openalex.org/W2294798173","https://openalex.org/W2591785087","https://openalex.org/W2891049628","https://openalex.org/W2901614569","https://openalex.org/W2908405708","https://openalex.org/W2979473749","https://openalex.org/W3018458124","https://openalex.org/W3093075953","https://openalex.org/W3099514962","https://openalex.org/W4292023222","https://openalex.org/W6609964338"],"related_works":["https://openalex.org/W2951493954","https://openalex.org/W2165173554","https://openalex.org/W2251843845","https://openalex.org/W2073182819","https://openalex.org/W2053566994","https://openalex.org/W2163875935","https://openalex.org/W2084311655","https://openalex.org/W3182675307","https://openalex.org/W202303397","https://openalex.org/W2124602215"],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2,24,44],"new":[3],"randomized":[4],"projection":[5,13,31,60,91],"method":[6],"based":[7],"on":[8,53],"entropy":[9,50],"optimization":[10],"of":[11,20,23,43,58,65,79,89],"random":[12],"matrices":[14,92],"(the":[15],"ERP":[16,36],"method).":[17],"The":[18],"concept":[19],"compactness":[21],"indicator":[22],"data":[25],"matrix,":[26],"which":[27],"is":[28,33,38,68],"stored":[29],"in":[30,40],"matrices,":[32],"introduced.":[34],"An":[35],"algorithm":[37],"formulated":[39],"the":[41,54,59,75,87,95],"form":[42],"conditional":[45],"maximization":[46],"problem":[47,67],"for":[48,74,86],"an":[49],"functional":[51],"defined":[52],"probability":[55,96],"density":[56,97],"functions":[57],"matrices.":[61],"A":[62],"discrete":[63],"version":[64],"this":[66],"considered,":[69],"and":[70,77],"conditions":[71],"are":[72,84],"obtained":[73],"existence":[76],"uniqueness":[78],"its":[80],"positive":[81],"solution.":[82],"Procedures":[83],"developed":[85],"implementation":[88],"entropy-optimal":[90],"by":[93],"sampling":[94],"functions.":[98]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
