{"id":"https://openalex.org/W1968785071","doi":"https://doi.org/10.1137/s0036144503437178","title":"Testing of Clustering","display_name":"Testing of Clustering","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W1968785071","doi":"https://doi.org/10.1137/s0036144503437178","mag":"1968785071"},"language":"en","primary_location":{"id":"doi:10.1137/s0036144503437178","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036144503437178","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Review","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"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/A5083469386","display_name":"Noga Alon","orcid":"https://orcid.org/0000-0003-1332-4883"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Noga Alon","raw_affiliation_strings":["Tel-Aviv  University"],"affiliations":[{"raw_affiliation_string":"Tel-Aviv  University","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112825682","display_name":"Seannie Dar","orcid":null},"institutions":[{"id":"https://openalex.org/I4210141777","display_name":"Academic College of Tel Aviv-Yafo","ror":"https://ror.org/04cg6c004","country_code":"IL","type":"education","lineage":["https://openalex.org/I4210141777"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Seannie Dar","raw_affiliation_strings":["Academic College of Tel-Aviv - Yaffo"],"affiliations":[{"raw_affiliation_string":"Academic College of Tel-Aviv - Yaffo","institution_ids":["https://openalex.org/I4210141777"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067484850","display_name":"Michal Parnas","orcid":"https://orcid.org/0000-0003-0189-6999"},"institutions":[{"id":"https://openalex.org/I4210141777","display_name":"Academic College of Tel Aviv-Yafo","ror":"https://ror.org/04cg6c004","country_code":"IL","type":"education","lineage":["https://openalex.org/I4210141777"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Michal Parnas","raw_affiliation_strings":["Academic College of Tel-Aviv - Yaffo"],"affiliations":[{"raw_affiliation_string":"Academic College of Tel-Aviv - Yaffo","institution_ids":["https://openalex.org/I4210141777"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063746987","display_name":"Dana Ron","orcid":"https://orcid.org/0000-0001-6576-7200"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Dana Ron","raw_affiliation_strings":["Tel-Aviv  University"],"affiliations":[{"raw_affiliation_string":"Tel-Aviv  University","institution_ids":["https://openalex.org/I16391192"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5083469386"],"corresponding_institution_ids":["https://openalex.org/I16391192"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.10870028,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"46","issue":"2","first_page":"285","last_page":"308"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T11106","display_name":"Data Management and Algorithms","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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":0.9926000237464905,"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/cluster-analysis","display_name":"Cluster analysis","score":0.7313277721405029},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.7257860898971558},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.671903133392334},{"id":"https://openalex.org/keywords/property-testing","display_name":"Property testing","score":0.6678918600082397},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6451268792152405},{"id":"https://openalex.org/keywords/cluster","display_name":"Cluster (spacecraft)","score":0.6245355606079102},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5416138768196106},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5019810199737549},{"id":"https://openalex.org/keywords/sample","display_name":"Sample (material)","score":0.4719357192516327},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.46117082238197327},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.461000919342041},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3985518217086792},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3647225499153137},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.31690600514411926},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2670992612838745},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1751914918422699},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.15486392378807068}],"concepts":[{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.7313277721405029},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.7257860898971558},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.671903133392334},{"id":"https://openalex.org/C123842658","wikidata":"https://www.wikidata.org/wiki/Q2918980","display_name":"Property testing","level":2,"score":0.6678918600082397},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6451268792152405},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.6245355606079102},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5416138768196106},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5019810199737549},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.4719357192516327},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.46117082238197327},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.461000919342041},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3985518217086792},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3647225499153137},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.31690600514411926},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2670992612838745},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1751914918422699},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.15486392378807068},{"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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036144503437178","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036144503437178","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Review","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310174","display_name":"University of Pittsburgh","ror":"https://ror.org/01an3r305"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W1965911513","https://openalex.org/W1967290069","https://openalex.org/W1970630090","https://openalex.org/W1973264045","https://openalex.org/W1980816908","https://openalex.org/W1983415430","https://openalex.org/W1988120018","https://openalex.org/W1993058867","https://openalex.org/W1996839061","https://openalex.org/W2000079459","https://openalex.org/W2013451793","https://openalex.org/W2018925011","https://openalex.org/W2036501955","https://openalex.org/W2044028871","https://openalex.org/W2054459484","https://openalex.org/W2055194501","https://openalex.org/W2068769655","https://openalex.org/W2072858942","https://openalex.org/W2073583237","https://openalex.org/W2075328466","https://openalex.org/W2083706862","https://openalex.org/W2086653003","https://openalex.org/W2092091787","https://openalex.org/W2109596848","https://openalex.org/W2115458940","https://openalex.org/W2139374679","https://openalex.org/W2148352980","https://openalex.org/W2161620758","https://openalex.org/W2161779238","https://openalex.org/W2165750745","https://openalex.org/W2171124048","https://openalex.org/W2611773579","https://openalex.org/W3008660429","https://openalex.org/W3023302315","https://openalex.org/W3101105133","https://openalex.org/W3137423196","https://openalex.org/W4235805661","https://openalex.org/W4238284510","https://openalex.org/W4256317935"],"related_works":["https://openalex.org/W267063485","https://openalex.org/W2073966617","https://openalex.org/W2963363569","https://openalex.org/W2160856947","https://openalex.org/W1972927969","https://openalex.org/W2108852611","https://openalex.org/W1566995037","https://openalex.org/W2949314693","https://openalex.org/W2404881703","https://openalex.org/W2358066991"],"abstract_inverted_index":{"In":[0,61,106,135,213],"this":[1,214],"work":[2,215],"we":[3,68,93,196,216],"study":[4],"the":[5,12,15,33,47,62,65,76,95,101,109,133,136,143,161,169,175,182,242,246,250,260,301,344,354],"problem":[6,96],"of":[7,24,52,64,83,97,103,138,163,168,225,234,245,262,278,295,300,315,325,331],"clustering":[8,98],"with":[9,30,249],"respect":[10,31],"to":[11,32,75,112,172,275,286,310,338,350,356],"diameter":[13,34],"and":[14,154,156,181,218,230,232,240,268],"radius":[16,66],"costs:":[17],"We":[18],"say":[19],"that":[20,46,70,73,130,198,209,221,305,319],"a":[21,81,115,119,223],"set":[22,162,261],"X":[23,37,178,185,207,264,304],"points":[25,53,72,164,202,247,263,302,341],"in":[26,54,228,303,328,342],"$\\Re^d$":[27],"is":[28,57,111,148,171,179,186,265,318],"$(k,b)-clusterable":[29],"cost":[35,67],"if":[36],"can":[38,158,282,347],"be":[39,79,126,204,256,273,284,348],"partitioned":[40],"into":[41],"k":[42,229],"subsets":[43],"(clusters)":[44],"so":[45,129,208],"distance":[48,82],"between":[49,174],"every":[50],"pair":[51],"each":[55],"cluster":[56,78,355],"at":[58,80,84],"most":[59,85],"b.":[60],"case":[63,176,183],"require":[69],"all":[71,277,296,340],"belong":[74],"same":[77],"b":[86],"for":[87],"some":[88],"common":[89],"central":[90],"point.":[91],"Here":[92],"approach":[94],"from":[99,160,188,193,206],"within":[100],"framework":[102],"property":[104,107,121],"testing.":[105],"testing,":[108],"goal":[110,167],"determine":[113],"whether":[114,123],"given":[116,149,359],"object":[117],"has":[118],"particular":[120],"or":[122],"it":[124,131,157,210,269],"should":[125,203],"modified":[127],"significantly":[128],"obtains":[132],"property.":[134],"context":[137],"clustering,":[139],"testing":[140],"takes":[141],"on":[142,238,241],"following":[144],"form:":[145],"The":[146,166,313],"algorithm":[147,170],"parameters":[150],"k,":[151],"b,":[152],"$\\beta$,":[153],"$\\epsilon$,":[155],"sample":[159,224],"X.":[165],"distinguish":[173],"when":[177,184,259],"(k,b)-clusterable":[180],"$\\epsilon$-far":[187,192],"being":[189,194],"$(k,\\bbeta)$-clusterable.":[190,212],"By":[191],"$(k,\\bbeta)$-clusterable":[195],"mean":[197],"more":[199],"than":[200],"$\\epsilon\\cdot|X|$":[201],"removed":[205],"becomes":[211],"describe":[217],"analyze":[219],"algorithms":[220,254,281,317],"use":[222],"size":[226],"polynomial":[227],"$1/\\epsilon$":[231],"independent":[233,330],"|X|.":[235,332],"(The":[236],"dependence":[237],"$\\beta$":[239],"dimension,":[243],"d,":[244],"varies":[248],"different":[251],"algorithms.)":[252],"Such":[253],"may":[255,270],"especially":[257],"useful":[258],"very":[266],"large":[267],"not":[271],"even":[272],"feasible":[274],"observe":[276],"it.":[279],"Our":[280],"also":[283],"used":[285,349],"find":[287],"approximately":[288],"good":[289],"clusterings.":[290],"Namely,":[291],"these":[292],"are":[293],"clusterings":[294,327],"but":[297],"an":[298,322],"$\\epsilon$-fraction":[299],"have":[306],"optimal":[307],"(or":[308],"close":[309],"optimal)":[311],"cost.":[312],"benefit":[314],"our":[316],"they":[320],"construct":[321],"implicit":[323,345],"representation":[324,346],"such":[326],"time":[329],"That":[333],"is,":[334],"without":[335],"actually":[336],"having":[337],"partition":[339],"X,":[343],"answer":[351],"queries":[352],"concerning":[353],"which":[357],"any":[358],"point":[360],"belongs.":[361]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}