{"id":"https://openalex.org/W15368807","doi":null,"title":"Finding low error clusterings","display_name":"Finding low error clusterings","publication_year":2009,"publication_date":"2009-12-01","ids":{"openalex":"https://openalex.org/W15368807","mag":"15368807"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.153.9296","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.153.9296","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.cmu.edu/~ninamf/papers/clusters09.pdf","raw_type":"text"},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"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/A5068544954","display_name":"Maria-Florina Balcan","orcid":"https://orcid.org/0000-0002-9525-0103","observed_orcids":["https://orcid.org/0000-0002-9525-0103"]},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Maria Florina Balcan","raw_affiliation_strings":["Microsoft , USA "],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Microsoft , USA ","institution_ids":["https://openalex.org/I1290206253"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042816355","display_name":"Mark Braverman","orcid":"https://orcid.org/0000-0003-1276-6081","observed_orcids":["https://orcid.org/0000-0003-1276-6081"]},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mark Braverman","raw_affiliation_strings":["Microsoft , USA "],"raw_orcid":"https://orcid.org/0000-0003-1276-6081","affiliations":[{"raw_affiliation_string":"Microsoft , USA ","institution_ids":["https://openalex.org/I1290206253"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I1290206253"],"apc_list":null,"apc_paid":null,"fwci":2.3126,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.88355647,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10637","display_name":"Advanced Clustering Algorithms Research","score":0.9570000171661377,"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/T10637","display_name":"Advanced Clustering Algorithms Research","score":0.9570000171661377,"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":0.029400000348687172,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.0013000000035390258,"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/clustering","display_name":"clustering","score":0.4320000112056732},{"id":"https://openalex.org/keywords/approximation-algorithms","display_name":"approximation algorithms","score":0.7139999866485596},{"id":"https://openalex.org/keywords/correlation-clustering","display_name":"correlation clustering","score":0.7329999804496765},{"id":"https://openalex.org/keywords/k-median","display_name":"k-median","score":0.8299999833106995},{"id":"https://openalex.org/keywords/k-means-clustering","display_name":"K-means clustering","score":0.9990000128746033},{"id":"https://openalex.org/keywords/transductive-learning","display_name":"transductive learning","score":0.6639999747276306},{"id":"https://openalex.org/keywords/inductive-learning","display_name":"inductive learning","score":0.9829999804496765},{"id":"https://openalex.org/keywords/np-hardness","display_name":"NP-hardness","score":0.6869999766349792},{"id":"https://openalex.org/keywords/pairwise-distances","display_name":"pairwise distances","score":0.3449999988079071}],"concepts":[{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.8393234014511108},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.6901537775993347},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.614500880241394},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5521242022514343},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5028335452079773},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.48522520065307617},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.4727821350097656},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.47016188502311707},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.45792728662490845},{"id":"https://openalex.org/C94641424","wikidata":"https://www.wikidata.org/wiki/Q5172845","display_name":"Correlation clustering","level":3,"score":0.44898325204849243},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4194050431251526},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3912794291973114},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3102099299430847},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3063355088233948},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.153.9296","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.153.9296","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.cmu.edu/~ninamf/papers/clusters09.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.162.2509","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.162.2509","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.mcgill.ca/~colt2009/papers/017.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.189.1758","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.189.1758","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.toronto.edu/%7Embraverm/Papers/clusters09.pdf","raw_type":"text"},{"id":"mag:15368807","doi":null,"is_oa":false,"landing_page_url":"https://www.cs.mcgill.ca/~colt2009/papers/017.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306418075","display_name":"Conference on Learning Theory","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"Conference on Learning Theory","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W305865050","https://openalex.org/W1500180658","https://openalex.org/W1503827365","https://openalex.org/W1535669030","https://openalex.org/W1564947197","https://openalex.org/W1574816920","https://openalex.org/W1605211498","https://openalex.org/W1950779386","https://openalex.org/W1956647075","https://openalex.org/W1969015668","https://openalex.org/W1970866964","https://openalex.org/W1974603499","https://openalex.org/W1980018091","https://openalex.org/W1994698869","https://openalex.org/W2001907516","https://openalex.org/W2003207175","https://openalex.org/W2006514056","https://openalex.org/W2020632401","https://openalex.org/W2050516752","https://openalex.org/W2085751730","https://openalex.org/W2095962154","https://openalex.org/W2110105238","https://openalex.org/W2111004121","https://openalex.org/W2124037793","https://openalex.org/W2129070834","https://openalex.org/W2141729166","https://openalex.org/W2143654071","https://openalex.org/W2167372977","https://openalex.org/W2171394996","https://openalex.org/W2799061466","https://openalex.org/W2914959486"],"related_works":["https://openalex.org/W1535669030","https://openalex.org/W2041504706","https://openalex.org/W4405036161","https://openalex.org/W2058681351","https://openalex.org/W45503606","https://openalex.org/W2326542235","https://openalex.org/W4289255343","https://openalex.org/W3109083552","https://openalex.org/W6959615350","https://openalex.org/W1994698869"],"abstract_inverted_index":{"A":[0],"common":[1],"approach":[2],"for":[3,76,106,123,160,178,191],"solving":[4],"clustering":[5,37,209],"problems":[6],"is":[7,40,51,61,89,135],"to":[8,11,62,86,91,116,131,186],"design":[9,187],"algorithms":[10,190],"approximately":[12],"optimize":[13],"various":[14],"objective":[15,78,88,133,145,162,221],"functions":[16,134],"(e.g.,":[17],"k-means":[18,108],"or":[19,29,225],"min-sum)":[20],"defined":[21],"in":[22,33,45,180,196,200],"terms":[23],"of":[24,119],"some":[25,41,55,77],"given":[26],"pairwise":[27,49],"distance":[28],"similarity":[30],"information.":[31],"However,":[32],"many":[34],"learning":[35],"motivated":[36],"applications":[38],"there":[39],"unknown":[42],"target":[43,93],"clustering;":[44],"such":[46,126],"cases":[47],"the":[48,58,67,92,107,143,153,156,197,201,207],"information":[50],"merely":[52],"based":[53],"on":[54,66],"heuristics":[56],"and":[57,109,172,183,199,214,222],"real":[59],"goal":[60],"achieve":[63],"low":[64,120],"error":[65],"data.":[68],"In":[69,95,138,166],"these":[70,132,185],"settings,":[71],"an":[72],"arbitrary":[73],"c-approximation":[74,85,130],"algorithm":[75],"would":[79],"work":[80,168],"well":[81],"only":[82],"if":[83],"any":[84],"that":[87,127],"close":[90],"clustering.":[94],"recent":[96],"work,":[97],"Balcan":[98],"et.":[99],"al":[100],"[8]":[101,150],"have":[102],"shown":[103],"how":[104],"both":[105,195],"k-median":[110],"objectives":[111],"this":[112,139,147,161,167,181,212,220],"property":[113],"allows":[114],"one":[115],"produce":[117],"clusterings":[118],"error,":[121],"even":[122],"values":[124],"c":[125],"getting":[128],"a":[129],"provably":[136],"NP-hard.":[137],"paper":[140],"we":[141,169],"analyze":[142,206],"min-sum":[144,154,179,226],"from":[146,211],"perspective.":[148],"While":[149],"also":[151,205],"considered":[152],"problem,":[155],"results":[157],"they":[158],"derived":[159],"were":[163],"substantially":[164],"weaker.":[165],"derive":[170],"new":[171],"much":[173],"more":[174],"subtle":[175],"structural":[176],"properties":[177],"context":[182],"use":[184],"highly":[188],"efficient":[189],"producing":[192],"accurate":[193],"clusterings,":[194],"transductive":[198],"inductive":[202],"case.":[203],"We":[204],"correlation":[208],"problem":[210],"perspective,":[213],"point":[215],"out":[216],"interesting":[217],"differences":[218],"between":[219],"k-median,":[223],"k-means,":[224],"objectives.":[227],"1":[228]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3}],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2016-06-24T00:00:00"}