{"id":"https://openalex.org/W4390187842","doi":"https://doi.org/10.1109/tit.2023.3346909","title":"The Power of Two Matrices in Spectral Algorithms for Community Recovery","display_name":"The Power of Two Matrices in Spectral Algorithms for Community Recovery","publication_year":2023,"publication_date":"2023-12-25","ids":{"openalex":"https://openalex.org/W4390187842","doi":"https://doi.org/10.1109/tit.2023.3346909"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2023.3346909","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2023.3346909","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://infoscience.epfl.ch/handle/20.500.14299/208291","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088062563","display_name":"Souvik Dhara","orcid":"https://orcid.org/0000-0001-8426-4529"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Souvik Dhara","raw_affiliation_strings":["School of Industrial Engineering, Purdue University, West Lafayette, IN, USA"],"raw_orcid":"https://orcid.org/0000-0001-8426-4529","affiliations":[{"raw_affiliation_string":"School of Industrial Engineering, Purdue University, West Lafayette, IN, USA","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073149598","display_name":"Julia Gaudio","orcid":"https://orcid.org/0000-0002-3078-1536"},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Julia Gaudio","raw_affiliation_strings":["Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL, USA"],"raw_orcid":"https://orcid.org/0000-0002-3078-1536","affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL, USA","institution_ids":["https://openalex.org/I111979921"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013467728","display_name":"Elchanan Mossel","orcid":"https://orcid.org/0000-0001-7812-7886"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Elchanan Mossel","raw_affiliation_strings":["Department of Mathematics, Massachussetts Institute of Technology, Cambridge, MA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Massachussetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035412316","display_name":"Colin Sandon","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Colin Sandon","raw_affiliation_strings":["Chair of Mathematical Data Science, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chair of Mathematical Data Science, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6345,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.74546451,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"70","issue":"5","first_page":"3599","last_page":"3621"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.9724000096321106,"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"}},"topics":[{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.9724000096321106,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.958299994468689,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.9567000269889832,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/stochastic-block-model","display_name":"Stochastic block model","score":0.6742017269134521},{"id":"https://openalex.org/keywords/spectral-graph-theory","display_name":"Spectral graph theory","score":0.5942842960357666},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5889805555343628},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5576980113983154},{"id":"https://openalex.org/keywords/spectral-clustering","display_name":"Spectral clustering","score":0.5007197856903076},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.4966004490852356},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4754102826118469},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4513508379459381},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.43372589349746704},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.4253784120082855},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.4240935444831848},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4127645492553711},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3885641098022461},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.24441567063331604},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.17015758156776428},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.16869771480560303},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.08011478185653687}],"concepts":[{"id":"https://openalex.org/C2779982251","wikidata":"https://www.wikidata.org/wiki/Q25053762","display_name":"Stochastic block model","level":3,"score":0.6742017269134521},{"id":"https://openalex.org/C74003402","wikidata":"https://www.wikidata.org/wiki/Q3180727","display_name":"Spectral graph theory","level":5,"score":0.5942842960357666},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5889805555343628},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5576980113983154},{"id":"https://openalex.org/C105611402","wikidata":"https://www.wikidata.org/wiki/Q2976589","display_name":"Spectral clustering","level":3,"score":0.5007197856903076},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.4966004490852356},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4754102826118469},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4513508379459381},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.43372589349746704},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.4253784120082855},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.4240935444831848},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4127645492553711},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3885641098022461},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.24441567063331604},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.17015758156776428},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.16869771480560303},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.08011478185653687},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2023.3346909","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2023.3346909","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:infoscience.epfl.ch:311366","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/208291","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:infoscience.epfl.ch:311366","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/208291","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"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4956351018","display_name":null,"funder_award_id":"DMS-1737944","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7855876414","display_name":null,"funder_award_id":"CCF-2154100","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1526954821","https://openalex.org/W1619721866","https://openalex.org/W1639593279","https://openalex.org/W1989042829","https://openalex.org/W2079035346","https://openalex.org/W2088272899","https://openalex.org/W2166163936","https://openalex.org/W2166602562","https://openalex.org/W2219655028","https://openalex.org/W2478722229","https://openalex.org/W2512500382","https://openalex.org/W2567866584","https://openalex.org/W2952469246","https://openalex.org/W2963660540","https://openalex.org/W3043617248","https://openalex.org/W4205528995","https://openalex.org/W4226310572","https://openalex.org/W4252323760","https://openalex.org/W6631561418","https://openalex.org/W6636424863","https://openalex.org/W6688335925","https://openalex.org/W6810777822"],"related_works":["https://openalex.org/W3124727659","https://openalex.org/W2136935487","https://openalex.org/W2032317191","https://openalex.org/W2902850141","https://openalex.org/W1955548541","https://openalex.org/W2265158691","https://openalex.org/W3168808485","https://openalex.org/W3017750840","https://openalex.org/W2607797544","https://openalex.org/W2130707516"],"abstract_inverted_index":{"Spectral":[0,39],"algorithms":[1,40,63,146],"are":[2,30,151],"some":[3,140],"of":[4,27,61,82,106,121,171,232],"the":[5,16,28,35,59,83,89,104,119,127,160,172,199,205,218,230],"main":[6],"tools":[7],"in":[8,67,111,126,155,187],"optimization":[9],"and":[10,23,25,51,86,153,204],"inference":[11],"problems":[12],"on":[13,148,178,214],"graphs.":[14,114],"Typically,":[15],"graph":[17,37,46,52,69,85],"is":[18,136,181,186],"encoded":[19],"as":[20],"a":[21,68,99,210],"matrix":[22,29,180,216],"eigenvectors":[24],"eigenvalues":[26],"then":[31,87],"used":[32,44],"to":[33,159,189],"solve":[34],"given":[36],"problem.":[38,71],"have":[41],"been":[42],"successfully":[43],"for":[45,103,168,198,229],"partitioning,":[47],"hidden":[48],"clique":[49],"recovery":[50],"coloring.":[53],"In":[54,115],"this":[55],"paper,":[56],"we":[57,117,165],"study":[58],"power":[60],"spectral":[62,90,101,145,175,211,233],"using":[64],"two":[65,74,79,95,149],"matrices":[66,76,150],"partitioning":[70],"We":[72,97,142,222],"use":[73],"different":[75,80],"resulting":[77],"from":[78,93],"encodings":[81],"same":[84],"combine":[88],"information":[91,161,219],"coming":[92],"these":[94],"matrices.":[96],"analyze":[98],"two-matrix":[100],"algorithm":[102,176,212],"problem":[105,120],"identifying":[107],"latent":[108],"community":[109,123],"structure":[110],"large":[112],"random":[113],"particular,":[116],"consider":[118],"recovering":[122,156],"assignments":[124],"exactly":[125],"censored":[128],"stochastic":[129],"block":[130],"model,":[131],"where":[132],"each":[133],"edge":[134],"status":[135],"revealed":[137],"independently":[138],"with":[139],"probability.":[141],"show":[143,166],"that":[144,167,197],"based":[147,177,213],"optimal":[152],"succeed":[154],"communities":[157],"up":[158],"theoretic":[162,220],"threshold.":[163,221],"Further,":[164],"most":[169],"choices":[170],"parameters,":[173],"any":[174],"one":[179,215],"suboptimal.":[182],"The":[183],"latter":[184],"observation":[185],"contrast":[188],"our":[190],"prior":[191],"works":[192],"(2022a,":[193],"2022b)":[194],"which":[195],"showed":[196],"symmetric":[200],"Stochastic":[201],"Block":[202],"Model":[203],"Planted":[206],"Dense":[207],"Subgraph":[208],"problem,":[209],"achieves":[217],"additionally":[223],"provide":[224],"more":[225],"general":[226],"geometric":[227],"conditions":[228],"(sub)-optimality":[231],"algorithms.":[234]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}