{"id":"https://openalex.org/W2061643070","doi":"https://doi.org/10.1109/cdc.2012.6426431","title":"Robust eigenvector of a stochastic matrix with application to PageRank","display_name":"Robust eigenvector of a stochastic matrix with application to PageRank","publication_year":2012,"publication_date":"2012-12-01","ids":{"openalex":"https://openalex.org/W2061643070","doi":"https://doi.org/10.1109/cdc.2012.6426431","mag":"2061643070"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2012.6426431","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2012.6426431","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE 51st IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1206.4897","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039659947","display_name":"Anatoli Juditsky","orcid":"https://orcid.org/0000-0001-5231-363X"},"institutions":[{"id":"https://openalex.org/I177483745","display_name":"Universit\u00e9 Joseph Fourier","ror":"https://ror.org/02aj0kh94","country_code":"FR","type":"education","lineage":["https://openalex.org/I177483745"]},{"id":"https://openalex.org/I4210149092","display_name":"Laboratoire Jean Kuntzmann","ror":"https://ror.org/04ett5b41","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I4210149092","https://openalex.org/I899635006","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I899635006","display_name":"Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/02rx3b187","country_code":"FR","type":"education","lineage":["https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Anatoli Juditsky","raw_affiliation_strings":["LJK, Universit\u00e9 J. Fourier, Grenoble, France","LJK, Universit\u00e9 J. Fourier, BP 51, 38041 Grenoble Cedex 09, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LJK, Universit\u00e9 J. Fourier, Grenoble, France","institution_ids":["https://openalex.org/I177483745","https://openalex.org/I4210149092","https://openalex.org/I899635006"]},{"raw_affiliation_string":"LJK, Universit\u00e9 J. Fourier, BP 51, 38041 Grenoble Cedex 09, France","institution_ids":["https://openalex.org/I177483745","https://openalex.org/I4210149092","https://openalex.org/I899635006"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032697658","display_name":"B. T. Polyak","orcid":"https://orcid.org/0000-0002-1898-2984"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Boris Polyak","raw_affiliation_strings":["Institute for Control Science, Moscow, Russia","Institute for Control Sciences, 65 Profsoyuznaya str., 117997 Moscow, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Control Science, Moscow, Russia","institution_ids":[]},{"raw_affiliation_string":"Institute for Control Sciences, 65 Profsoyuznaya str., 117997 Moscow, Russia","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"3171","last_page":"3176"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"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/T11182","display_name":"Auction Theory and Applications","score":0.987500011920929,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"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/T10991","display_name":"Game Theory and Voting Systems","score":0.9785000085830688,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/pagerank","display_name":"PageRank","score":0.8580143451690674},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7297453284263611},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6322262287139893},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.5576660633087158},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.524289071559906},{"id":"https://openalex.org/keywords/ranking","display_name":"Ranking (information retrieval)","score":0.5070884227752686},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.49217596650123596},{"id":"https://openalex.org/keywords/power-iteration","display_name":"Power iteration","score":0.4756224453449249},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.46955424547195435},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41765671968460083},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.416882187128067},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36169278621673584},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16812008619308472},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.15778031945228577},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.07680681347846985}],"concepts":[{"id":"https://openalex.org/C2779172887","wikidata":"https://www.wikidata.org/wiki/Q184316","display_name":"PageRank","level":2,"score":0.8580143451690674},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7297453284263611},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6322262287139893},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.5576660633087158},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.524289071559906},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.5070884227752686},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.49217596650123596},{"id":"https://openalex.org/C162443888","wikidata":"https://www.wikidata.org/wiki/Q1426504","display_name":"Power iteration","level":3,"score":0.4756224453449249},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46955424547195435},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41765671968460083},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.416882187128067},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36169278621673584},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16812008619308472},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.15778031945228577},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.07680681347846985},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"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},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1109/cdc.2012.6426431","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2012.6426431","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE 51st IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1206.4897","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1206.4897","pdf_url":"https://arxiv.org/pdf/1206.4897","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"","raw_type":"text"},{"id":"mag:2061643070","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1206.4897.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.758.1364","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.758.1364","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1206.4897.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00981872v1","is_oa":false,"landing_page_url":"https://hal.science/hal-00981872","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"CDC 2012 - IEEE 51st Annual Conference on Decision and Control, Dec 2012, Maui, United States. pp.3171-3176, ⟨10.1109/CDC.2012.6426431⟩","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"doi:10.48550/arxiv.1206.4897","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1206.4897","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1206.4897","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1206.4897","pdf_url":"https://arxiv.org/pdf/1206.4897","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W92732855","https://openalex.org/W1608412409","https://openalex.org/W1995042628","https://openalex.org/W2020929673","https://openalex.org/W2021798600","https://openalex.org/W2048679451","https://openalex.org/W2066636486","https://openalex.org/W2089105401","https://openalex.org/W2094140553","https://openalex.org/W2102573976","https://openalex.org/W2106101949","https://openalex.org/W2118921825","https://openalex.org/W2174883827","https://openalex.org/W2271295020","https://openalex.org/W3125041190","https://openalex.org/W6649374121","https://openalex.org/W6656954120","https://openalex.org/W6679440081"],"related_works":["https://openalex.org/W2963951770","https://openalex.org/W2891857568","https://openalex.org/W2442014075","https://openalex.org/W2907570585","https://openalex.org/W2266817871","https://openalex.org/W1978359677","https://openalex.org/W2982168727","https://openalex.org/W2530665635","https://openalex.org/W3136756258","https://openalex.org/W2909116885","https://openalex.org/W2952283347","https://openalex.org/W3195737265","https://openalex.org/W2274921471","https://openalex.org/W2556047458","https://openalex.org/W3190854671","https://openalex.org/W3134041587","https://openalex.org/W3039860230","https://openalex.org/W1927286929","https://openalex.org/W2206137099","https://openalex.org/W2616806001"],"abstract_inverted_index":{"We":[0,49],"discuss":[1],"a":[2,9,30,45,52,64,69],"definition":[3],"of":[4,8,11],"robust":[5,31,39,56],"dominant":[6],"eigenvector":[7,40,57],"family":[10],"stochastic":[12],"matrices.":[13],"Our":[14],"focus":[15],"is":[16,42],"on":[17],"application":[18],"to":[19,33,44],"ranking":[20],"problems,":[21],"where":[22],"the":[23,34],"proposed":[24],"approach":[25],"can":[26,60],"be":[27,61],"seen":[28],"as":[29,63],"alternative":[32],"standard":[35],"PageRank":[36],"technique.":[37],"The":[38],"computation":[41],"reduced":[43],"convex":[46],"optimization":[47],"problem.":[48],"also":[50],"propose":[51],"simple":[53],"algorithm":[54],"for":[55],"approximation":[58],"which":[59],"viewed":[62],"regularized":[65],"power":[66],"method":[67],"with":[68],"special":[70],"stopping":[71],"rule.":[72]},"counts_by_year":[{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}