{"id":"https://openalex.org/W3090078726","doi":"https://doi.org/10.20382/jocg.v11i1a11","title":"An improved cost function for hierarchical cluster trees","display_name":"An improved cost function for hierarchical cluster trees","publication_year":2019,"publication_date":"2019-01-14","ids":{"openalex":"https://openalex.org/W3090078726","doi":"https://doi.org/10.20382/jocg.v11i1a11","mag":"3090078726"},"language":"en","primary_location":{"id":"pmh:oai:ojs.library.carleton.ca:article/3101","is_oa":true,"landing_page_url":"https://jocg.org/index.php/jocg/article/view/3101","pdf_url":"https://jocg.org/index.php/jocg/article/view/3101","source":{"id":"https://openalex.org/S4306400962","display_name":"Journal of Computational Geometry (Carleton University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67031392","host_organization_name":"Carleton University","host_organization_lineage":["https://openalex.org/I67031392"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Computational Geometry; Vol. 11 No. 1 (2020); 283\u2013331","raw_type":"info:eu-repo/semantics/article"},"type":"article","indexed_in":["datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://jocg.org/index.php/jocg/article/view/3101","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027458220","display_name":"Dingkang Wang","orcid":"https://orcid.org/0000-0002-3888-9250"},"institutions":[{"id":"https://openalex.org/I52357470","display_name":"The Ohio State University","ror":"https://ror.org/00rs6vg23","country_code":"US","type":"education","lineage":["https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wang, Dingkang","raw_affiliation_strings":["the Ohio State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"the Ohio State University","institution_ids":["https://openalex.org/I52357470"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101536052","display_name":"Yusu Wang","orcid":"https://orcid.org/0000-0001-7950-4348"},"institutions":[{"id":"https://openalex.org/I52357470","display_name":"The Ohio State University","ror":"https://ror.org/00rs6vg23","country_code":"US","type":"education","lineage":["https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wang, Yusu","raw_affiliation_strings":["the Ohio State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"the Ohio State University","institution_ids":["https://openalex.org/I52357470"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I52357470"],"apc_list":null,"apc_paid":null,"fwci":0.1412,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.616352,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"11","issue":"1","first_page":"283","last_page":"331"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10637","display_name":"Advanced Clustering Algorithms Research","score":0.9987999796867371,"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":0.9987999796867371,"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9884999990463257,"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/hierarchical-clustering","display_name":"Hierarchical clustering","score":0.7168428897857666},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.6913139820098877},{"id":"https://openalex.org/keywords/granularity","display_name":"Granularity","score":0.6197038888931274},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.5474694967269897},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5348834991455078},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5126411318778992},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5077134370803833},{"id":"https://openalex.org/keywords/similarity","display_name":"Similarity (geometry)","score":0.4994070529937744},{"id":"https://openalex.org/keywords/tree-structure","display_name":"Tree structure","score":0.4640006422996521},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42949995398521423},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4160151779651642},{"id":"https://openalex.org/keywords/hierarchical-clustering-of-networks","display_name":"Hierarchical clustering of networks","score":0.4109070301055908},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.3594937026500702},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.326477974653244},{"id":"https://openalex.org/keywords/correlation-clustering","display_name":"Correlation clustering","score":0.26319289207458496},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.25771546363830566},{"id":"https://openalex.org/keywords/cure-data-clustering-algorithm","display_name":"CURE data clustering algorithm","score":0.1840420365333557},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16117578744888306},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12244981527328491}],"concepts":[{"id":"https://openalex.org/C92835128","wikidata":"https://www.wikidata.org/wiki/Q1277447","display_name":"Hierarchical clustering","level":3,"score":0.7168428897857666},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.6913139820098877},{"id":"https://openalex.org/C177774035","wikidata":"https://www.wikidata.org/wiki/Q1246948","display_name":"Granularity","level":2,"score":0.6197038888931274},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5474694967269897},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5348834991455078},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5126411318778992},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5077134370803833},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.4994070529937744},{"id":"https://openalex.org/C163797641","wikidata":"https://www.wikidata.org/wiki/Q2067937","display_name":"Tree structure","level":3,"score":0.4640006422996521},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42949995398521423},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4160151779651642},{"id":"https://openalex.org/C82261393","wikidata":"https://www.wikidata.org/wiki/Q17038699","display_name":"Hierarchical clustering of networks","level":5,"score":0.4109070301055908},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3594937026500702},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.326477974653244},{"id":"https://openalex.org/C94641424","wikidata":"https://www.wikidata.org/wiki/Q5172845","display_name":"Correlation clustering","level":3,"score":0.26319289207458496},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.25771546363830566},{"id":"https://openalex.org/C33704608","wikidata":"https://www.wikidata.org/wiki/Q5014717","display_name":"CURE data clustering algorithm","level":4,"score":0.1840420365333557},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16117578744888306},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12244981527328491},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"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/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","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},{"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:ojs.library.carleton.ca:article/3101","is_oa":true,"landing_page_url":"https://jocg.org/index.php/jocg/article/view/3101","pdf_url":"https://jocg.org/index.php/jocg/article/view/3101","source":{"id":"https://openalex.org/S4306400962","display_name":"Journal of Computational Geometry (Carleton University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67031392","host_organization_name":"Carleton University","host_organization_lineage":["https://openalex.org/I67031392"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Computational Geometry; Vol. 11 No. 1 (2020); 283\u2013331","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:aa9db065f1664869842b3e09e1207b38","is_oa":true,"landing_page_url":"https://doaj.org/article/aa9db065f1664869842b3e09e1207b38","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Computational Geometry, Vol 11, Iss 1 (2020)","raw_type":"article"},{"id":"doi:10.20382/jocg.v11i1a11","is_oa":true,"landing_page_url":"https://doi.org/10.20382/jocg.v11i1a11","pdf_url":null,"source":{"id":"https://openalex.org/S4306400962","display_name":"Journal of Computational Geometry (Carleton University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67031392","host_organization_name":"Carleton University","host_organization_lineage":["https://openalex.org/I67031392"],"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-journal"},{"id":"mag:3090078726","is_oa":true,"landing_page_url":"https://dblp.uni-trier.de/db/journals/corr/corr1812.html#abs-1812-02715","pdf_url":null,"source":{"id":"https://openalex.org/S78224298","display_name":"Journal of computational geometry","issn_l":"1920-180X","issn":["1920-180X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313061","host_organization_name":"Carleton University","host_organization_lineage":["https://openalex.org/P4310313061"],"host_organization_lineage_names":["Carleton University"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Journal of computational geometry","raw_type":null}],"best_oa_location":{"id":"pmh:oai:ojs.library.carleton.ca:article/3101","is_oa":true,"landing_page_url":"https://jocg.org/index.php/jocg/article/view/3101","pdf_url":"https://jocg.org/index.php/jocg/article/view/3101","source":{"id":"https://openalex.org/S4306400962","display_name":"Journal of Computational Geometry (Carleton University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67031392","host_organization_name":"Carleton University","host_organization_lineage":["https://openalex.org/I67031392"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Computational Geometry; Vol. 11 No. 1 (2020); 283\u2013331","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1302751805","display_name":"RI: Small: Learning discrete structure from continuous spaces","funder_award_id":"1815697","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2137412393","display_name":null,"funder_award_id":"DMS-1547357","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3187039853","display_name":null,"funder_award_id":"RI-1815697","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4229663209","display_name":"RTG: Algebraic Topology and Its Applications","funder_award_id":"1547357","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6367296400","display_name":"TRIPODS: Topology, Geometry, and Data Analysis (TGDA@OSU):Discovering Structure, Shape, and Dynamics in Data","funder_award_id":"1740761","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309374","display_name":"Ohio State University","ror":"https://ror.org/00rs6vg23"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3090078726.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2903468495","https://openalex.org/W2606287509","https://openalex.org/W2752002846","https://openalex.org/W3090602628","https://openalex.org/W3034838735","https://openalex.org/W2753345952","https://openalex.org/W2204093302","https://openalex.org/W2782833507","https://openalex.org/W2809201693","https://openalex.org/W1987600084","https://openalex.org/W2108201615","https://openalex.org/W3132069259","https://openalex.org/W1611855301","https://openalex.org/W2993574280","https://openalex.org/W2889658189","https://openalex.org/W1997612870","https://openalex.org/W3189074906","https://openalex.org/W1975023024","https://openalex.org/W2082021920","https://openalex.org/W118394218"],"abstract_inverted_index":{"Hierarchical":[0],"clustering":[1,40,73,92,109],"has":[2,121,247,303,316],"been":[3,122],"a":[4,14,18,26,43,51,54,81,150,154,158,179,187,237,248,257,289,304,317],"popular":[5],"method":[6],"in":[7,76,80,251,266],"various":[8],"data":[9,15,33,44,61],"analysis":[10],"applications.":[11],"It":[12],"partitions":[13],"set":[16,45],"into":[17],"hierarchical":[19,39,72,91,108,180],"collection":[20],"of":[21,29,42,98,135,163,224,236,281,325],"clusters,":[22],"and":[23,62,100,132,243,268],"can":[24,46],"provide":[25,322],"global":[27],"view":[28],"(cluster)":[30],"structure":[31],"behind":[32],"across":[34],"different":[35],"granularity":[36],"levels.":[37],"A":[38],"(HC)":[41],"be":[47,273],"naturally":[48],"represented":[49],"by":[50,330],"tree,":[52],"called":[53],"HC-tree,":[55],"where":[56],"leaves":[57],"correspond":[58,68],"to":[59,69,88,178,199,288,293],"input":[60,173,301,313],"subtrees":[63],"rooted":[64],"at":[65,148],"internal":[66],"nodes":[67],"clusters.":[70],"Many":[71],"algorithms":[74],"used":[75],"practice":[77],"are":[78],"developed":[79,193],"procedure":[82],"manner.":[83],"In":[84,182],"[9],":[85],"Dasgupta":[86],"proposed":[87],"study":[89],"the":[90,136,161,207,212,215,222,233,252,269,283,295,300,312,326],"problem":[93],"from":[94,153,338],"an":[95,102,172,308,339],"optimization":[96],"point":[97],"view,":[99],"introduced":[101],"intuitive":[103],"cost":[104,144,165,189,197,209,219,226,235,271,284,328],"function":[105,145,166,210,227,285,329],"for":[106,157,334],"similarity-based":[107],"with":[110,262],"nice":[111],"properties":[112],"as":[113,115,214],"well":[114,171],"natural":[116],"approximation":[117,128,309],"algorithms.":[118],"There":[119],"since":[120],"several":[123],"followup":[124],"work":[125],"on":[126,195],"better":[127],"algorithms,":[129],"hardness":[130],"analysis,":[131],"general":[133],"understanding":[134,324],"objective":[137],"functions.":[138],"We":[139],"observe":[140],"that":[141,254,259],"while":[142],"Dasgupta's":[143,196,218],"is":[146,176,192,228,260],"effective":[147],"differentiating":[149],"good":[151],"HC-tree":[152,258],"bad":[155],"one":[156,216],"fixed":[159],"graph,":[160],"value":[162,223],"this":[164,183,201],"does":[167],"not":[168],"reflect":[169],"how":[170],"similarity":[174],"graph":[175,238,302,314],"consistent":[177,261],"structure.":[181],"paper,":[184],"we":[185,321],"present":[186],"new":[188,208,279,327],"function,":[190,198],"which":[191],"based":[194],"address":[200],"issue.":[202],"The":[203,278],"optimal":[204,234,270,296],"tree":[205,298],"under":[206,217],"remains":[211],"same":[213],"function.":[220],"However,":[221],"our":[225],"more":[229],"meaningful.":[230],"For":[231],"example,":[232],"$G$":[239,246],"equals":[240],"$1$":[241,276],"if":[242,245],"only":[244],"perfect":[249,305,318],"HC-structure":[250],"sense":[253],"there":[255],"exists":[256],"all":[263],"triplets":[264],"relations":[265],"$G$;":[267],"will":[272],"larger":[274],"than":[275],"otherwise.":[277],"way":[280],"formulating":[282],"also":[286],"leads":[287],"polynomial":[290],"time":[291],"algorithm":[292,310],"compute":[294],"cluster":[297],"when":[299,311],"HC-structure,":[306],"or":[307],"almost":[315],"HC-structure.":[319],"Finally,":[320],"further":[323],"studying":[331],"its":[332],"behavior":[333],"random":[335],"graphs":[336],"sampled":[337],"edge":[340],"probability":[341],"matrix.":[342]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T06:51:31.235846","created_date":"2025-10-10T00:00:00"}