{"id":"https://openalex.org/W4283155227","doi":"https://doi.org/10.1080/10618600.2022.2091575","title":"<i>K</i>-CDFs: A Nonparametric Clustering Algorithm via Cumulative Distribution Function","display_name":"<i>K</i>-CDFs: A Nonparametric Clustering Algorithm via Cumulative Distribution Function","publication_year":2022,"publication_date":"2022-06-20","ids":{"openalex":"https://openalex.org/W4283155227","doi":"https://doi.org/10.1080/10618600.2022.2091575"},"language":"en","primary_location":{"id":"doi:10.1080/10618600.2022.2091575","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10618600.2022.2091575","pdf_url":null,"source":{"id":"https://openalex.org/S76159266","display_name":"Journal of Computational and Graphical Statistics","issn_l":"1061-8600","issn":["1061-8600","1537-2715"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational and Graphical Statistics","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/A5051903409","display_name":"Jicai Liu","orcid":"https://orcid.org/0000-0003-1467-9782"},"institutions":[{"id":"https://openalex.org/I146613903","display_name":"Shanghai Lixin University of Accounting and Finance","ror":"https://ror.org/02g81yf77","country_code":"CN","type":"education","lineage":["https://openalex.org/I146613903"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jicai Liu","raw_affiliation_strings":["School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai, China;;"],"raw_orcid":"https://orcid.org/0000-0003-1467-9782","affiliations":[{"raw_affiliation_string":"School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai, China;;","institution_ids":["https://openalex.org/I146613903"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100754914","display_name":"Jinhong Li","orcid":"https://orcid.org/0000-0003-1981-9449"},"institutions":[{"id":"https://openalex.org/I66867065","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67","country_code":"CN","type":"education","lineage":["https://openalex.org/I66867065"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jinhong Li","raw_affiliation_strings":["School of Statistics, East China Normal University, Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Statistics, East China Normal University, Shanghai, China","institution_ids":["https://openalex.org/I66867065"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008413852","display_name":"Riquan Zhang","orcid":"https://orcid.org/0000-0001-5206-5568"},"institutions":[{"id":"https://openalex.org/I66867065","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67","country_code":"CN","type":"education","lineage":["https://openalex.org/I66867065"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Riquan Zhang","raw_affiliation_strings":["School of Statistics, East China Normal University, Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Statistics, East China Normal University, Shanghai, China","institution_ids":["https://openalex.org/I66867065"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5051903409"],"corresponding_institution_ids":["https://openalex.org/I146613903"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.05916244,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"32","issue":"1","first_page":"304","last_page":"318"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9998999834060669,"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":0.9998999834060669,"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/T10637","display_name":"Advanced Clustering Algorithms Research","score":0.9983000159263611,"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/T11106","display_name":"Data Management and Algorithms","score":0.9483000040054321,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/cumulative-distribution-function","display_name":"Cumulative distribution function","score":0.7118542194366455},{"id":"https://openalex.org/keywords/nonparametric-statistics","display_name":"Nonparametric statistics","score":0.6852642893791199},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.6732128262519836},{"id":"https://openalex.org/keywords/univariate","display_name":"Univariate","score":0.6589627265930176},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5352749228477478},{"id":"https://openalex.org/keywords/empirical-distribution-function","display_name":"Empirical distribution function","score":0.5146694779396057},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5077141523361206},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.48441416025161743},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4399976134300232},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41829055547714233},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33105385303497314},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.281853049993515},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.20006775856018066},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.08095130324363708}],"concepts":[{"id":"https://openalex.org/C103784038","wikidata":"https://www.wikidata.org/wiki/Q386228","display_name":"Cumulative distribution function","level":3,"score":0.7118542194366455},{"id":"https://openalex.org/C102366305","wikidata":"https://www.wikidata.org/wiki/Q1097688","display_name":"Nonparametric statistics","level":2,"score":0.6852642893791199},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.6732128262519836},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.6589627265930176},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5352749228477478},{"id":"https://openalex.org/C98385598","wikidata":"https://www.wikidata.org/wiki/Q1339385","display_name":"Empirical distribution function","level":2,"score":0.5146694779396057},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5077141523361206},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.48441416025161743},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4399976134300232},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41829055547714233},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33105385303497314},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.281853049993515},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.20006775856018066},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.08095130324363708},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10618600.2022.2091575","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10618600.2022.2091575","pdf_url":null,"source":{"id":"https://openalex.org/S76159266","display_name":"Journal of Computational and Graphical Statistics","issn_l":"1061-8600","issn":["1061-8600","1537-2715"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational and Graphical Statistics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2331517647","display_name":null,"funder_award_id":"11501372","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3709438092","display_name":null,"funder_award_id":"11971018","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G387334962","display_name":"\u5206\u5e03\u5f0f\u7edf\u8ba1\u8ba1\u7b97\u65b9\u6cd5\u548c\u7406\u8bba\u82e5\u5e72\u7814\u7a76","funder_award_id":"11971171","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6582392765","display_name":null,"funder_award_id":"11426156","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7962219275","display_name":null,"funder_award_id":"11571112","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1779010541","https://openalex.org/W1986007546","https://openalex.org/W1996881001","https://openalex.org/W2011832962","https://openalex.org/W2071949631","https://openalex.org/W2086943813","https://openalex.org/W2121947440","https://openalex.org/W2129964859","https://openalex.org/W2140095548","https://openalex.org/W2141786611","https://openalex.org/W2150593711","https://openalex.org/W2155074104","https://openalex.org/W2155754954","https://openalex.org/W2299467264","https://openalex.org/W2795076630","https://openalex.org/W2887804548","https://openalex.org/W2914933231","https://openalex.org/W2999905431","https://openalex.org/W3104433444","https://openalex.org/W3111931804","https://openalex.org/W3173981744","https://openalex.org/W4235169531","https://openalex.org/W6745956461"],"related_works":["https://openalex.org/W4317940328","https://openalex.org/W2161853176","https://openalex.org/W2386296695","https://openalex.org/W2050364510","https://openalex.org/W4323319894","https://openalex.org/W2017388630","https://openalex.org/W4291960776","https://openalex.org/W4283325019","https://openalex.org/W2018141282","https://openalex.org/W1979334856"],"abstract_inverted_index":{"We":[0,131],"propose":[1,113],"a":[2,118,127],"novel":[3],"partitioning":[4],"clustering":[5],"procedure":[6,43,76],"based":[7],"on":[8,51,99],"the":[9,19,22,33,38,65,91,110,122,133,138],"cumulative":[10],"distribution":[11],"function":[12],"(CDF),":[13],"called":[14],"K-CDFs.":[15],"For":[16],"univariate":[17,68],"data,":[18,86],"K-CDFs":[20,66],"represent":[21],"cluster":[23,52],"centers":[24],"by":[25,37,55],"empirical":[26,145],"CDFs":[27],"and":[28,46,101,126,144],"assign":[29],"each":[30],"observation":[31],"to":[32,63,70,84,90],"closest":[34],"center":[35],"measured":[36],"Crame\u00b4r-von":[39],"Mises":[40],"distance.":[41],"The":[42,74],"is":[44,61,82,87],"nonparametric":[45],"does":[47,94],"not":[48,88,95],"require":[49,96],"assumptions":[50],"distributions":[53],"imposed":[54],"mixture":[56],"models.":[57],"A":[58],"projection":[59],"technique":[60],"used":[62],"generalize":[64],"for":[67,153],"data":[69,92,100],"an":[71],"arbitrary":[72],"dimension.":[73],"proposed":[75,139],"has":[77],"several":[78,148],"appealing":[79],"properties.":[80],"It":[81],"robust":[83],"heavy-tailed":[85],"sensitive":[89],"dimensions,":[93],"moment":[97],"conditions":[98],"can":[102],"effectively":[103],"detect":[104],"linearly":[105],"nonseparable":[106],"clusters.":[107],"To":[108],"implement":[109],"K-CDFs,":[111],"we":[112],"two":[114],"kinds":[115],"of":[116,137,147],"algorithms:":[117],"greedy":[119],"algorithm":[120,125],"as":[121],"classical":[123],"Lloyd\u2019s":[124],"spectral":[128],"relaxation":[129],"algorithm.":[130],"illustrate":[132],"finite":[134],"sample":[135],"performance":[136],"algorithms":[140],"through":[141],"simulation":[142],"experiments":[143],"analyses":[146],"real":[149],"datasets.":[150],"Supplementary":[151],"files":[152],"this":[154],"article":[155],"are":[156],"available":[157],"online.":[158]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-06-06T09:05:17.133730","created_date":"2025-10-10T00:00:00"}