{"id":"https://openalex.org/W2791707368","doi":"https://doi.org/10.4230/lipics.icalp.2018.57","title":"Semi-Supervised Algorithms for Approximately Optimal and Accurate Clustering","display_name":"Semi-Supervised Algorithms for Approximately Optimal and Accurate Clustering","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2791707368","doi":"https://doi.org/10.4230/lipics.icalp.2018.57","mag":"2791707368"},"language":"en","primary_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:9061","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.57","pdf_url":null,"source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"InProceedings"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.57","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049102663","display_name":"Buddhima Gamlath","orcid":null},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Gamlath, Buddhima","raw_affiliation_strings":["\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland"],"affiliations":[{"raw_affiliation_string":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047872044","display_name":"Sangxia Huang","orcid":null},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]},{"id":"https://openalex.org/I4210102622","display_name":"Mobile Heights (Sweden)","ror":"https://ror.org/016cc6840","country_code":"SE","type":"company","lineage":["https://openalex.org/I4210102622"]}],"countries":["CH","SE"],"is_corresponding":false,"raw_author_name":"Huang, Sangxia","raw_affiliation_strings":["Sony Mobile Communications, Lund, Sweden","\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland"],"affiliations":[{"raw_affiliation_string":"Sony Mobile Communications, Lund, Sweden","institution_ids":["https://openalex.org/I4210102622"]},{"raw_affiliation_string":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046999727","display_name":"Ola Svensson","orcid":"https://orcid.org/0000-0003-2997-1372"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Svensson, Ola","raw_affiliation_strings":["\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland"],"affiliations":[{"raw_affiliation_string":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5049102663"],"corresponding_institution_ids":["https://openalex.org/I5124864"],"apc_list":null,"apc_paid":null,"fwci":0.3385,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.6689068,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"14","last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9951000213623047,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9951000213623047,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9868000149726868,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9818000197410583,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/combinatorics","display_name":"Combinatorics","score":0.7068749666213989},{"id":"https://openalex.org/keywords/oracle","display_name":"Oracle","score":0.6893976926803589},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.6700772047042847},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.6228483319282532},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5909380316734314},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5596855878829956},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.5364974141120911},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.5321521162986755},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.44884711503982544},{"id":"https://openalex.org/keywords/cluster","display_name":"Cluster (spacecraft)","score":0.4271519184112549},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42332300543785095},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4139620065689087},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3734899163246155},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23694512248039246},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08861804008483887},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0693255066871643}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7068749666213989},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.6893976926803589},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.6700772047042847},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.6228483319282532},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5909380316734314},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5596855878829956},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.5364974141120911},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.5321521162986755},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.44884711503982544},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.4271519184112549},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42332300543785095},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4139620065689087},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3734899163246155},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23694512248039246},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08861804008483887},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0693255066871643},{"id":"https://openalex.org/C115903868","wikidata":"https://www.wikidata.org/wiki/Q80993","display_name":"Software engineering","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"pmh:oai:drops-oai.dagstuhl.de:9061","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.57","pdf_url":null,"source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"InProceedings"},{"id":"pmh:oai:arXiv.org:1803.00926","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1803.00926","pdf_url":"https://arxiv.org/pdf/1803.00926","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":null,"raw_type":"text"},{"id":"mag:2791707368","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1803.00926","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":"doi:10.48550/arxiv.1803.00926","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1803.00926","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":"article"},{"id":"mag:2963505742","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/1803.00926.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":null,"is_accepted":false,"is_published":null,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.4230/lipics.icalp.2018.57","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.icalp.2018.57","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":[],"is_oa":false,"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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":""}],"best_oa_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:9061","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.57","pdf_url":null,"source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"InProceedings"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W607505555","https://openalex.org/W2018165630","https://openalex.org/W2091283109","https://openalex.org/W2171125141","https://openalex.org/W2187617524","https://openalex.org/W2199495299","https://openalex.org/W2313395524","https://openalex.org/W2404136910","https://openalex.org/W2613497313"],"related_works":["https://openalex.org/W2963505742","https://openalex.org/W3081671930","https://openalex.org/W3120910628","https://openalex.org/W2900282949","https://openalex.org/W2951296787","https://openalex.org/W3081680577","https://openalex.org/W2960682810","https://openalex.org/W2626428686","https://openalex.org/W2949644106","https://openalex.org/W3094501518","https://openalex.org/W2266908258","https://openalex.org/W2953282389","https://openalex.org/W2782820392","https://openalex.org/W1950779386","https://openalex.org/W2991693986","https://openalex.org/W3127119670","https://openalex.org/W3194261387","https://openalex.org/W3203778961","https://openalex.org/W2951038604","https://openalex.org/W1497325939"],"abstract_inverted_index":{"We":[0,74,131,153,205],"study":[1],"$k$-means":[2,141,160,220],"clustering":[3,42,81],"in":[4,22,118,143,149,169,218,247],"a":[5,23,41,53,80,109,185],"semi-supervised":[6],"setting.":[7],"Given":[8],"an":[9,66,105,177],"oracle":[10,34,95,203],"that":[11,133,190,208,240,255],"returns":[12],"whether":[13],"two":[14],"given":[15],"points":[16,84],"belong":[17],"to":[18,38,77],"the":[19,29,62,98,119,125,158,165,170,174,209,225,228,248,260,264],"same":[20],"cluster":[21,129],"fixed":[24],"optimal":[25,63],"clustering,":[26],"we":[27,162,183,238],"investigate":[28],"following":[30],"question:":[31],"how":[32,76],"many":[33],"queries":[35,212],"are":[36],"sufficient":[37],"efficiently":[39],"recover":[40],"that,":[43,156],"with":[44,85,104],"probability":[45,111],"at":[46,56,69,173,243],"least":[47,70,244],"$(1":[48,58,71,215],"-":[49,72,216],"\u03b4)$,":[50],"simultaneously":[51],"has":[52],"cost":[54,64],"of":[55,68,127,176,211,227,250],"most":[57],"+":[59,194,197],"\u03b5)$":[60],"times":[61],"and":[65,108,146,232],"accuracy":[67],"\u03b5)$?":[73],"show":[75,132,155,207,239],"achieve":[78],"such":[79],"on":[82,167,180,224,263],"$n$":[83,168],"$O{((k^2":[86],"\\log":[87],"n)":[88],"\\cdot":[89,199],"m{(Q,":[90],"\u03b5^4,":[91],"\u03b4/":[92],"(k\\log":[93],"n))})}$":[94],"queries,":[96],"when":[97],"$k$":[99],"clusters":[100],"can":[101,163],"be":[102,245],"learned":[103],"$\u03b5'$":[106],"error":[107],"failure":[110],"$\u03b4'$":[112],"using":[113],"$m(Q,":[114,134],"\u03b5',\u03b4')$":[115],"labeled":[116],"samples":[117],"supervised":[120],"setting,":[121],"where":[122],"$Q$":[123],"is":[124,137],"set":[126],"candidate":[128,251],"centers.":[130,252],"\u03b5',":[135],"\u03b4')$":[136],"small":[138],"both":[139],"for":[140,147,157,214,233],"instances":[142],"Euclidean":[144,159,219,230],"space":[145,236],"those":[148],"finite":[150,234],"metric":[151,235],"spaces.":[152],"further":[154],"instances,":[161],"avoid":[164],"dependency":[166,179],"query":[171,257],"complexity":[172],"expense":[175],"increased":[178],"$k$:":[181],"specifically,":[182],"give":[184],"slightly":[186],"more":[187],"involved":[188],"algorithm":[189],"uses":[191],"$O(k^4/(\u03b5^2":[192],"\u03b4)":[193],"(k^{9}/\u03b5^4)":[195],"\\log(1/\u03b4)":[196],"k":[198],"m(\\mathbb{R}^r,":[200],"\u03b5^4/k,":[201],"\u03b4))$":[202],"queries.":[204],"also":[206],"number":[210,249],"needed":[213],"\u03b5)$-accuracy":[217],"must":[221,242],"linearly":[222],"depend":[223],"dimension":[226],"underlying":[229],"space,":[231],"$k$-means,":[237],"it":[241],"logarithmic":[246],"This":[253],"shows":[254],"our":[256],"complexities":[258],"capture":[259],"right":[261],"dependencies":[262],"respective":[265],"parameters.":[266]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}