{"id":"https://openalex.org/W3134305631","doi":"https://doi.org/10.1109/tit.2021.3063155","title":"Cutoff for Exact Recovery of Gaussian Mixture Models","display_name":"Cutoff for Exact Recovery of Gaussian Mixture Models","publication_year":2021,"publication_date":"2021-03-02","ids":{"openalex":"https://openalex.org/W3134305631","doi":"https://doi.org/10.1109/tit.2021.3063155","mag":"3134305631"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2021.3063155","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tit.2021.3063155","pdf_url":"https://ieeexplore.ieee.org/ielx7/18/9437270/09366690.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":"hybrid","oa_url":"https://ieeexplore.ieee.org/ielx7/18/9437270/09366690.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100375174","display_name":"Xiaohui Chen","orcid":"https://orcid.org/0000-0003-1418-8190"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xiaohui Chen","raw_affiliation_strings":["Department of Statistics, University of Illinois at Urbana-Champaign, Champaign, IL, USA"],"raw_orcid":"https://orcid.org/0000-0003-1418-8190","affiliations":[{"raw_affiliation_string":"Department of Statistics, University of Illinois at Urbana-Champaign, Champaign, IL, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5104208065","display_name":"Yun Yang","orcid":"https://orcid.org/0000-0002-4523-5829"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yun Yang","raw_affiliation_strings":["Department of Statistics, University of Illinois at Urbana-Champaign, Champaign, IL, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, University of Illinois at Urbana-Champaign, Champaign, IL, USA","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":1.0919,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.80914204,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"67","issue":"6","first_page":"4223","last_page":"4238"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9994000196456909,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9994000196456909,"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":0.9958999752998352,"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"}},{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9944000244140625,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.7298557162284851},{"id":"https://openalex.org/keywords/cutoff","display_name":"Cutoff","score":0.6892958283424377},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.6855934858322144},{"id":"https://openalex.org/keywords/cluster","display_name":"Cluster (spacecraft)","score":0.6793183088302612},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.6686732172966003},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.5485261082649231},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5428140759468079},{"id":"https://openalex.org/keywords/mixture-model","display_name":"Mixture model","score":0.5097422003746033},{"id":"https://openalex.org/keywords/independent-component-analysis","display_name":"Independent component analysis","score":0.5025911331176758},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4936893880367279},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.41129812598228455},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33938103914260864},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3391414284706116},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3207889199256897},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.31368786096572876},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3117457926273346},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.21819299459457397},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19978907704353333},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15585088729858398},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0787331759929657}],"concepts":[{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.7298557162284851},{"id":"https://openalex.org/C2778217198","wikidata":"https://www.wikidata.org/wiki/Q556977","display_name":"Cutoff","level":2,"score":0.6892958283424377},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.6855934858322144},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.6793183088302612},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.6686732172966003},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.5485261082649231},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5428140759468079},{"id":"https://openalex.org/C61224824","wikidata":"https://www.wikidata.org/wiki/Q2260434","display_name":"Mixture model","level":2,"score":0.5097422003746033},{"id":"https://openalex.org/C51432778","wikidata":"https://www.wikidata.org/wiki/Q1259145","display_name":"Independent component analysis","level":2,"score":0.5025911331176758},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4936893880367279},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.41129812598228455},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33938103914260864},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3391414284706116},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3207889199256897},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31368786096572876},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3117457926273346},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.21819299459457397},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19978907704353333},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15585088729858398},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0787331759929657},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2021.3063155","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tit.2021.3063155","pdf_url":"https://ieeexplore.ieee.org/ielx7/18/9437270/09366690.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1109/tit.2021.3063155","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tit.2021.3063155","pdf_url":"https://ieeexplore.ieee.org/ielx7/18/9437270/09366690.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2975797254","display_name":null,"funder_award_id":"DMS-1907316","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3540664297","display_name":null,"funder_award_id":"DMS-1752614","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G3686253567","display_name":"Fast and Robust Gaussian Process Inference for Bayesian Nonparametric Learning","funder_award_id":"1907316","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G511767067","display_name":"CAREER: Computer-Intensive Statistical Inference on High-Dimensional and Massive Data: From Theoretical Foundations to Practical Computations","funder_award_id":"1752614","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7021217349","display_name":null,"funder_award_id":"DMS-1752614","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"},{"id":"https://openalex.org/F4320309369","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44"},{"id":"https://openalex.org/F4320332222","display_name":"University of Illinois at Urbana-Champaign","ror":"https://ror.org/047426m28"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3134305631.pdf","grobid_xml":"https://content.openalex.org/works/W3134305631.grobid-xml"},"referenced_works_count":101,"referenced_works":["https://openalex.org/W93530381","https://openalex.org/W593611996","https://openalex.org/W1509689762","https://openalex.org/W1520260139","https://openalex.org/W1560153690","https://openalex.org/W1574816920","https://openalex.org/W1903051497","https://openalex.org/W1980018091","https://openalex.org/W1986219860","https://openalex.org/W1986790896","https://openalex.org/W2002276939","https://openalex.org/W2010353172","https://openalex.org/W2010656511","https://openalex.org/W2011832962","https://openalex.org/W2016776056","https://openalex.org/W2023348178","https://openalex.org/W2024514015","https://openalex.org/W2029698681","https://openalex.org/W2049633694","https://openalex.org/W2051638434","https://openalex.org/W2059971059","https://openalex.org/W2060195349","https://openalex.org/W2066459155","https://openalex.org/W2073459066","https://openalex.org/W2086943813","https://openalex.org/W2097752597","https://openalex.org/W2102907934","https://openalex.org/W2103718624","https://openalex.org/W2127218421","https://openalex.org/W2132914434","https://openalex.org/W2133755908","https://openalex.org/W2150593711","https://openalex.org/W2162521241","https://openalex.org/W2165874743","https://openalex.org/W2167930540","https://openalex.org/W2171009857","https://openalex.org/W2187617524","https://openalex.org/W2302206641","https://openalex.org/W2344998188","https://openalex.org/W2432836740","https://openalex.org/W2509532045","https://openalex.org/W2516692117","https://openalex.org/W2523553400","https://openalex.org/W2531902758","https://openalex.org/W2560270297","https://openalex.org/W2567866584","https://openalex.org/W2616604195","https://openalex.org/W2769553966","https://openalex.org/W2793533891","https://openalex.org/W2805892743","https://openalex.org/W2884993474","https://openalex.org/W2911808754","https://openalex.org/W2922491876","https://openalex.org/W2942673878","https://openalex.org/W2962737134","https://openalex.org/W2963103132","https://openalex.org/W2963105348","https://openalex.org/W2963264680","https://openalex.org/W2963455969","https://openalex.org/W2963496884","https://openalex.org/W2963545258","https://openalex.org/W2963626260","https://openalex.org/W2963814147","https://openalex.org/W2963919656","https://openalex.org/W2964073168","https://openalex.org/W2965497096","https://openalex.org/W2970227627","https://openalex.org/W3037883861","https://openalex.org/W3098833389","https://openalex.org/W3100129515","https://openalex.org/W3100144903","https://openalex.org/W3101273398","https://openalex.org/W3105809221","https://openalex.org/W3110475465","https://openalex.org/W3113313164","https://openalex.org/W3116640826","https://openalex.org/W4205585032","https://openalex.org/W4205648292","https://openalex.org/W4250954493","https://openalex.org/W4293482053","https://openalex.org/W4300167232","https://openalex.org/W4301903793","https://openalex.org/W6603787252","https://openalex.org/W6649743962","https://openalex.org/W6668990524","https://openalex.org/W6674297765","https://openalex.org/W6678914141","https://openalex.org/W6684578312","https://openalex.org/W6685061373","https://openalex.org/W6686507408","https://openalex.org/W6718186988","https://openalex.org/W6725272734","https://openalex.org/W6726062340","https://openalex.org/W6727129644","https://openalex.org/W6737809643","https://openalex.org/W6746403984","https://openalex.org/W6751768991","https://openalex.org/W6761871856","https://openalex.org/W6765952306","https://openalex.org/W6767408179","https://openalex.org/W6777828175"],"related_works":["https://openalex.org/W2121429698","https://openalex.org/W2182042810","https://openalex.org/W4252230435","https://openalex.org/W55679925","https://openalex.org/W3080404860","https://openalex.org/W3092388660","https://openalex.org/W1778838665","https://openalex.org/W2046761971","https://openalex.org/W3144722888","https://openalex.org/W2089650474"],"abstract_inverted_index":{"We":[0],"determine":[1],"the":[2,37,50],"information-theoretic":[3],"cutoff":[4],"value":[5],"on":[6],"separation":[7],"of":[8,14,36,52],"cluster":[9,15,25,53],"centers":[10],"for":[11,45],"exact":[12,46],"recovery":[13,47],"labels":[16],"in":[17],"a":[18,31],"K-component":[19],"Gaussian":[20],"mixture":[21],"model":[22],"with":[23],"equal":[24],"sizes.":[26],"Moreover,":[27],"we":[28],"show":[29],"that":[30],"semidefinite":[32],"programming":[33],"(SDP)":[34],"relaxation":[35],"K-means":[38],"clustering":[39],"method":[40],"achieves":[41],"such":[42],"sharp":[43],"threshold":[44],"without":[48],"assuming":[49],"symmetry":[51],"centers.":[54]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}