{"id":"https://openalex.org/W2007149844","doi":"https://doi.org/10.1109/isda.2011.6121777","title":"Extending external validity measures for determining the number of clusters","display_name":"Extending external validity measures for determining the number of clusters","publication_year":2011,"publication_date":"2011-11-01","ids":{"openalex":"https://openalex.org/W2007149844","doi":"https://doi.org/10.1109/isda.2011.6121777","mag":"2007149844"},"language":"en","primary_location":{"id":"doi:10.1109/isda.2011.6121777","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isda.2011.6121777","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 11th International Conference on Intelligent Systems Design and Applications","raw_type":"proceedings-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/A5055909810","display_name":"Qinpei Zhao","orcid":"https://orcid.org/0000-0002-1765-1171"},"institutions":[{"id":"https://openalex.org/I175532246","display_name":"University of Eastern Finland","ror":"https://ror.org/00cyydd11","country_code":"FI","type":"education","lineage":["https://openalex.org/I175532246"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Qinpei Zhao","raw_affiliation_strings":["School of Computing, University of Eastern Finland, Joensuu, Finland","School Of Computing, University of Eastern Finland, Joensuu, Finland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computing, University of Eastern Finland, Joensuu, Finland","institution_ids":["https://openalex.org/I175532246"]},{"raw_affiliation_string":"School Of Computing, University of Eastern Finland, Joensuu, Finland","institution_ids":["https://openalex.org/I175532246"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109832004","display_name":"Mantao Xu","orcid":null},"institutions":[{"id":"https://openalex.org/I4210156189","display_name":"Shanghai Dianji University","ror":"https://ror.org/055fene14","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210156189"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mantao Xu","raw_affiliation_strings":["School of Electronics & Information, Shanghai Dianji University, Shanghai, China","School of Electronics & Information, Shanghai Dian Ji University, Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electronics & Information, Shanghai Dianji University, Shanghai, China","institution_ids":["https://openalex.org/I4210156189"]},{"raw_affiliation_string":"School of Electronics & Information, Shanghai Dian Ji University, Shanghai, China","institution_ids":["https://openalex.org/I4210156189"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037846871","display_name":"Pasi Fr\u00e4nti","orcid":"https://orcid.org/0000-0002-9554-2827"},"institutions":[{"id":"https://openalex.org/I175532246","display_name":"University of Eastern Finland","ror":"https://ror.org/00cyydd11","country_code":"FI","type":"education","lineage":["https://openalex.org/I175532246"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Pasi Franti","raw_affiliation_strings":["School of Computing, University of Eastern Finland, Joensuu, Finland","School Of Computing, University of Eastern Finland, Joensuu, Finland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computing, University of Eastern Finland, Joensuu, Finland","institution_ids":["https://openalex.org/I175532246"]},{"raw_affiliation_string":"School Of Computing, University of Eastern Finland, Joensuu, Finland","institution_ids":["https://openalex.org/I175532246"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3189,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.83788324,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"931","last_page":"936"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10637","display_name":"Advanced Clustering Algorithms Research","score":0.9993000030517578,"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":0.9993000030517578,"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/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.9959999918937683,"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"}},{"id":"https://openalex.org/T11550","display_name":"Text and Document Classification Technologies","score":0.9940999746322632,"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/resampling","display_name":"Resampling","score":0.8244810104370117},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.7340850830078125},{"id":"https://openalex.org/keywords/cluster","display_name":"Cluster (spacecraft)","score":0.624358594417572},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6150792837142944},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.49886274337768555},{"id":"https://openalex.org/keywords/unsupervised-learning","display_name":"Unsupervised learning","score":0.459574431180954},{"id":"https://openalex.org/keywords/external-validity","display_name":"External validity","score":0.42789602279663086},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.40451595187187195},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.39480167627334595},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.332085520029068},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1966821253299713}],"concepts":[{"id":"https://openalex.org/C150921843","wikidata":"https://www.wikidata.org/wiki/Q1170431","display_name":"Resampling","level":2,"score":0.8244810104370117},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.7340850830078125},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.624358594417572},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6150792837142944},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.49886274337768555},{"id":"https://openalex.org/C8038995","wikidata":"https://www.wikidata.org/wiki/Q1152135","display_name":"Unsupervised learning","level":2,"score":0.459574431180954},{"id":"https://openalex.org/C174106493","wikidata":"https://www.wikidata.org/wiki/Q1057880","display_name":"External validity","level":2,"score":0.42789602279663086},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.40451595187187195},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.39480167627334595},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.332085520029068},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1966821253299713},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"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":1,"locations":[{"id":"doi:10.1109/isda.2011.6121777","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isda.2011.6121777","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 11th International Conference on Intelligent Systems Design and Applications","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Quality Education","score":0.5199999809265137,"id":"https://metadata.un.org/sdg/4"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1604366459","https://openalex.org/W1852582905","https://openalex.org/W2030644393","https://openalex.org/W2033403400","https://openalex.org/W2062696711","https://openalex.org/W2071949631","https://openalex.org/W2076864249","https://openalex.org/W2108343180","https://openalex.org/W2113054345","https://openalex.org/W2121189958","https://openalex.org/W2129630294","https://openalex.org/W2135705692","https://openalex.org/W2137631287","https://openalex.org/W2146261447","https://openalex.org/W2167972246","https://openalex.org/W2963673689","https://openalex.org/W3120740533","https://openalex.org/W3143185366","https://openalex.org/W4244030505","https://openalex.org/W4255554660","https://openalex.org/W6639038281","https://openalex.org/W6788247690","https://openalex.org/W7011740287"],"related_works":["https://openalex.org/W2052515325","https://openalex.org/W2050948537","https://openalex.org/W2767646790","https://openalex.org/W2352041579","https://openalex.org/W1488006380","https://openalex.org/W1998176685","https://openalex.org/W2138381686","https://openalex.org/W2141585124","https://openalex.org/W3123883311","https://openalex.org/W2032175896"],"abstract_inverted_index":{"External":[0],"validity":[1,48,87],"measures":[2,49,88],"in":[3,30,92,120,144],"cluster":[4,39,132],"analysis":[5],"evaluate":[6],"how":[7],"well":[8],"the":[9,18,27,31,46,68,73,81,122,127,138,146],"clustering":[10],"results":[11,135],"match":[12],"to":[13,25],"a":[14,57,93],"prior":[15,28,62],"knowledge":[16,29],"about":[17],"data.":[19],"However,":[20],"it":[21],"is":[22,64,115,141],"always":[23],"intractable":[24],"get":[26],"practical":[32],"problem":[33,128],"of":[34,96,110,124,129,148],"unsupervised":[35,130],"learning,":[36,131],"such":[37],"as":[38],"analysis.":[40,133],"In":[41],"this":[42],"paper,":[43],"we":[44,76],"extend":[45],"external":[47,86],"for":[50,89,126],"both":[51],"hard":[52],"and":[53,118],"soft":[54,90],"partitions":[55,91],"by":[56,72],"resampling":[58,74],"method,":[59,75],"where":[60],"no":[61],"information":[63],"needed.":[65],"To":[66],"lighten":[67],"time":[69,95,108],"burden":[70],"caused":[71],"incorporate":[77],"two":[78],"approaches":[79],"into":[80],"proposed":[82,113,139],"method:":[83],"(i)":[84],"extending":[85],"computational":[94],"O(M":[97],"<sup":[98],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[99],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[100],"N);":[101],"(ii)":[102],"an":[103],"efficient":[104],"sub-sampling":[105],"method":[106,114,140],"with":[107],"complexity":[109],"O(N).":[111],"The":[112],"then":[116],"applied":[117],"reviewed":[119],"determining":[121],"number":[123,147],"clusters":[125],"Experimental":[134],"has":[136],"demonstrated":[137],"very":[142],"effective":[143],"solving":[145],"clusters.":[149]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}