{"id":"https://openalex.org/W2074647706","doi":"https://doi.org/10.1016/s1571-0661(05)80060-x","title":"Clusters, Concepts, and Pseudometrics","display_name":"Clusters, Concepts, and Pseudometrics","publication_year":2001,"publication_date":"2001-03-01","ids":{"openalex":"https://openalex.org/W2074647706","doi":"https://doi.org/10.1016/s1571-0661(05)80060-x","mag":"2074647706"},"language":"en","primary_location":{"id":"doi:10.1016/s1571-0661(05)80060-x","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(05)80060-x","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.1016/s1571-0661(05)80060-x","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081498801","display_name":"Michael Rice","orcid":"https://orcid.org/0000-0001-5150-4792"},"institutions":[{"id":"https://openalex.org/I100538780","display_name":"Wesleyan University","ror":"https://ror.org/05h7xva58","country_code":"US","type":"education","lineage":["https://openalex.org/I100538780"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Michael D. Rice","raw_affiliation_strings":[".a Department of Mathematics & Computer Science Wesleyan University Middletown, CT, 06459"],"affiliations":[{"raw_affiliation_string":".a Department of Mathematics & Computer Science Wesleyan University Middletown, CT, 06459","institution_ids":["https://openalex.org/I100538780"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049442429","display_name":"Michael Siff","orcid":null},"institutions":[{"id":"https://openalex.org/I56327960","display_name":"Sarah Lawrence College","ror":"https://ror.org/04sxj4848","country_code":"US","type":"education","lineage":["https://openalex.org/I56327960"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Michael Siff","raw_affiliation_strings":["Faculty of Computer Science Sarah Lawrence College Bronxville, New York, 10708"],"affiliations":[{"raw_affiliation_string":"Faculty of Computer Science Sarah Lawrence College Bronxville, New York, 10708","institution_ids":["https://openalex.org/I56327960"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5049442429","https://openalex.org/A5081498801"],"corresponding_institution_ids":["https://openalex.org/I100538780","https://openalex.org/I56327960"],"apc_list":null,"apc_paid":null,"fwci":0.457,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.67312633,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"40","issue":null,"first_page":"323","last_page":"346"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.9689000248908997,"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/T10637","display_name":"Advanced Clustering Algorithms Research","score":0.9485999941825867,"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/cardinality","display_name":"Cardinality (data modeling)","score":0.6361480355262756},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.6175963878631592},{"id":"https://openalex.org/keywords/binary-relation","display_name":"Binary relation","score":0.5635794401168823},{"id":"https://openalex.org/keywords/formal-concept-analysis","display_name":"Formal concept analysis","score":0.5213842988014221},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.499281644821167},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4941301643848419},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.48684924840927124},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4389268159866333},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.4388960599899292},{"id":"https://openalex.org/keywords/cluster","display_name":"Cluster (spacecraft)","score":0.42987900972366333},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41349658370018005},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.28096210956573486},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2670772075653076},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13155177235603333}],"concepts":[{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.6361480355262756},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.6175963878631592},{"id":"https://openalex.org/C65180967","wikidata":"https://www.wikidata.org/wiki/Q130901","display_name":"Binary relation","level":2,"score":0.5635794401168823},{"id":"https://openalex.org/C76363472","wikidata":"https://www.wikidata.org/wiki/Q1437394","display_name":"Formal concept analysis","level":2,"score":0.5213842988014221},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.499281644821167},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4941301643848419},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.48684924840927124},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4389268159866333},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.4388960599899292},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.42987900972366333},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41349658370018005},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.28096210956573486},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2670772075653076},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13155177235603333},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1016/s1571-0661(05)80060-x","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(05)80060-x","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.196.8419","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.196.8419","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www1.elsevier.com/gej-ng/31/29/23/97/27/58/40032.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.21.9360","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.21.9360","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://mrice.web.wesleyan.edu/irishpaper.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1016/s1571-0661(05)80060-x","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(05)80060-x","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1503729935","https://openalex.org/W1969502877","https://openalex.org/W1972645849","https://openalex.org/W2047555270","https://openalex.org/W2060389467","https://openalex.org/W2065060195","https://openalex.org/W2071515776","https://openalex.org/W2093397547","https://openalex.org/W2118587067","https://openalex.org/W2124961838","https://openalex.org/W2281963798","https://openalex.org/W2612166593","https://openalex.org/W4300885858","https://openalex.org/W6643219146","https://openalex.org/W6666760815","https://openalex.org/W6678419004","https://openalex.org/W6695412920"],"related_works":["https://openalex.org/W4253128163","https://openalex.org/W2891818416","https://openalex.org/W2003123666","https://openalex.org/W2602662326","https://openalex.org/W2103222807","https://openalex.org/W2090935781","https://openalex.org/W2408706506","https://openalex.org/W116479447","https://openalex.org/W2246930433","https://openalex.org/W1978080601"],"abstract_inverted_index":{"The":[0,235],"fields":[1],"of":[2,22,39,61,100,107,120,126,140,154,161,190,197,206,220,231,246,261,263,272,279,297],"cluster":[3],"analysis":[4,7,17,29,189,205,230],"and":[5,64,76,84,88,122,168,182,199,226,229,274],"concept":[6,102,111,127,301],"are":[8,86,163,179,282],"both":[9],"used":[10],"to":[11,91,252],"identify":[12],"patterns":[13],"in":[14,110,118,138,176,269],"data.":[15],"Concept":[16],"identifies":[18],"similarities":[19],"between":[20,47],"sets":[21,162],"objects":[23,31,62],"based":[24,35,129],"on":[25,36,58,130,194,223,240],"their":[26],"attributes.":[27],"Cluster":[28],"groups":[30],"with":[32,133],"related":[33],"characteristics":[34],"some":[37],"notion":[38],"distance.":[40],"In":[41,51,113],"this":[42],"paper,":[43],"we":[44,66,115],"investigate":[45],"connections":[46],"these":[48],"two":[49],"approaches.":[50],"particular,":[52,114],"for":[53,292],"each":[54,166,174],"binary":[55],"relation":[56],"defined":[57,172],"a":[59,93,98,124,134,213,244,276,289,294,298],"set":[60,74],"O":[63,273],"attributes,":[65],"define":[67],"distance":[68],"functions":[69],"\u03c1":[70,83,121,198],"(on":[71,78],"the":[72,101,147,152,170,177,188,191,195,204,207,218,221,227,232,259,264,270,285],"power":[73],"of)":[75],"\u03b4":[77,85],"O).":[79],"We":[80,210],"prove":[81],"that":[82,96,216,258,281],"pseudometrics":[87],"use":[89],"them":[90],"specify":[92],"clustering":[94,143,265],"algorithm":[95,144,178,192,222,236,266,286],"computes":[97],"subset":[99,296],"lattice":[103],"discover":[104],"new":[105],"interpretations":[106],"basic":[108],"notions":[109],"analysis.":[112],"characterize":[116,123],"concepts":[117],"terms":[119,139],"family":[125],"lattices":[128],"all":[131],"subsets":[132],"fixed":[135],"cardinality":[136],"bound":[137],"\u03b4.":[141],"Our":[142,255],"differs":[145],"from":[146,243,249],"classical":[148,208],"algorithms":[149],"since,":[150],"first,":[151],"values":[153],"\u03c1,":[155],"not":[156,184],"\u03b4,":[157],"determine":[158],"which":[159],"pairs":[160],"combined":[164],"at":[165,173],"level,":[167],"second,":[169],"clusters":[171,280],"level":[175],"generally":[180],"anti-chains":[181],"may":[183],"be":[185,288],"partitions.":[186],"Therefore,":[187],"depends":[193],"metric-geometry":[196],"is":[200,267],"more":[201],"involved":[202],"than":[203],"algorithms.":[209],"have":[211],"developed":[212],"software":[214],"environment":[215],"permits":[217],"execution":[219],"finite":[224],"relations":[225,241],"storage":[228],"resulting":[233],"clusters.":[234],"has":[237],"been":[238],"run":[239],"generated":[242],"variety":[245],"sources":[247],"ranging":[248],"medical":[250],"research":[251],"sporting":[253],"events.":[254],"results":[256],"indicate":[257],"number":[260,278],"iterations":[262],"linear":[268,277],"size":[271],"produces":[275],"concepts.":[283],"Hence":[284],"can":[287],"useful":[290],"tool":[291],"computing":[293],"tractable":[295],"very":[299],"large":[300],"lattice.":[302]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}