{"id":"https://openalex.org/W2737180220","doi":"https://doi.org/10.1007/s00357-018-9274-x","title":"Three-Way Symbolic Tree-Maps and Ultrametrics","display_name":"Three-Way Symbolic Tree-Maps and Ultrametrics","publication_year":2018,"publication_date":"2018-10-31","ids":{"openalex":"https://openalex.org/W2737180220","doi":"https://doi.org/10.1007/s00357-018-9274-x","mag":"2737180220"},"language":"en","primary_location":{"id":"doi:10.1007/s00357-018-9274-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00357-018-9274-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00357-018-9274-x.pdf","source":{"id":"https://openalex.org/S73028643","display_name":"Journal of Classification","issn_l":"0176-4268","issn":["0176-4268","1432-1343"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Classification","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00357-018-9274-x.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007694498","display_name":"Katharina T. Huber","orcid":"https://orcid.org/0000-0002-6368-7511"},"institutions":[{"id":"https://openalex.org/I2799300731","display_name":"Norwich Research Park","ror":"https://ror.org/0062dz060","country_code":"GB","type":"archive","lineage":["https://openalex.org/I2799300731"]},{"id":"https://openalex.org/I1118541","display_name":"University of East Anglia","ror":"https://ror.org/026k5mg93","country_code":"GB","type":"education","lineage":["https://openalex.org/I1118541"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Katharina T. Huber","raw_affiliation_strings":["University of East Anglia, Norwich Research Park, Norwich, NR4 7TJ, UK","University of East Anglia,  Norwich, UK"],"affiliations":[{"raw_affiliation_string":"University of East Anglia, Norwich Research Park, Norwich, NR4 7TJ, UK","institution_ids":["https://openalex.org/I1118541","https://openalex.org/I2799300731"]},{"raw_affiliation_string":"University of East Anglia,  Norwich, UK","institution_ids":["https://openalex.org/I1118541"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042929579","display_name":"Vincent Moulton","orcid":"https://orcid.org/0000-0001-9371-6435"},"institutions":[{"id":"https://openalex.org/I1118541","display_name":"University of East Anglia","ror":"https://ror.org/026k5mg93","country_code":"GB","type":"education","lineage":["https://openalex.org/I1118541"]},{"id":"https://openalex.org/I2799300731","display_name":"Norwich Research Park","ror":"https://ror.org/0062dz060","country_code":"GB","type":"archive","lineage":["https://openalex.org/I2799300731"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Vincent Moulton","raw_affiliation_strings":["University of East Anglia, Norwich Research Park, Norwich, NR4 7TJ, UK","University of East Anglia,  Norwich, UK"],"affiliations":[{"raw_affiliation_string":"University of East Anglia, Norwich Research Park, Norwich, NR4 7TJ, UK","institution_ids":["https://openalex.org/I1118541","https://openalex.org/I2799300731"]},{"raw_affiliation_string":"University of East Anglia,  Norwich, UK","institution_ids":["https://openalex.org/I1118541"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035173636","display_name":"Guillaume E. Scholz","orcid":"https://orcid.org/0000-0001-5033-8040"},"institutions":[{"id":"https://openalex.org/I1118541","display_name":"University of East Anglia","ror":"https://ror.org/026k5mg93","country_code":"GB","type":"education","lineage":["https://openalex.org/I1118541"]},{"id":"https://openalex.org/I2799300731","display_name":"Norwich Research Park","ror":"https://ror.org/0062dz060","country_code":"GB","type":"archive","lineage":["https://openalex.org/I2799300731"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Guillaume E. Scholz","raw_affiliation_strings":["University of East Anglia, Norwich Research Park, Norwich, NR4 7TJ, UK","University of East Anglia,  Norwich, UK"],"affiliations":[{"raw_affiliation_string":"University of East Anglia, Norwich Research Park, Norwich, NR4 7TJ, UK","institution_ids":["https://openalex.org/I1118541","https://openalex.org/I2799300731"]},{"raw_affiliation_string":"University of East Anglia,  Norwich, UK","institution_ids":["https://openalex.org/I1118541"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5007694498"],"corresponding_institution_ids":["https://openalex.org/I1118541","https://openalex.org/I2799300731"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.07089319,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9800000190734863,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9800000190734863,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9746000170707703,"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":0.9681000113487244,"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/ultrametric-space","display_name":"Ultrametric space","score":0.8355868458747864},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.616611897945404},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.6074973940849304},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.517488956451416},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.45406126976013184},{"id":"https://openalex.org/keywords/the-symbolic","display_name":"The Symbolic","score":0.4466724395751953},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3979329466819763},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34517014026641846},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34015312790870667},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.09737670421600342}],"concepts":[{"id":"https://openalex.org/C61067352","wikidata":"https://www.wikidata.org/wiki/Q1897429","display_name":"Ultrametric space","level":3,"score":0.8355868458747864},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.616611897945404},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.6074973940849304},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.517488956451416},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.45406126976013184},{"id":"https://openalex.org/C2776095079","wikidata":"https://www.wikidata.org/wiki/Q489538","display_name":"The Symbolic","level":2,"score":0.4466724395751953},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3979329466819763},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34517014026641846},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34015312790870667},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.09737670421600342},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"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/C11171543","wikidata":"https://www.wikidata.org/wiki/Q41630","display_name":"Psychoanalysis","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1007/s00357-018-9274-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00357-018-9274-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00357-018-9274-x.pdf","source":{"id":"https://openalex.org/S73028643","display_name":"Journal of Classification","issn_l":"0176-4268","issn":["0176-4268","1432-1343"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Classification","raw_type":"journal-article"},{"id":"pmh:oai:ueaeprints.uea.ac.uk:65297","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400384","display_name":"UEA Digital Repository (University of East Anglia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1118541","host_organization_name":"University of East Anglia","host_organization_lineage":["https://openalex.org/I1118541"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},{"id":"pmh:oai:arXiv.org:1707.08010","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1707.08010","pdf_url":"https://arxiv.org/pdf/1707.08010","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2737180220","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1707.08010","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:RePEc:spr:jclass:v:36:y:2019:i:3:d:10.1007_s00357-018-9274-x","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s00357-018-9274-x","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"doi:10.48550/arxiv.1707.08010","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1707.08010","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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"}],"best_oa_location":{"id":"doi:10.1007/s00357-018-9274-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00357-018-9274-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00357-018-9274-x.pdf","source":{"id":"https://openalex.org/S73028643","display_name":"Journal of Classification","issn_l":"0176-4268","issn":["0176-4268","1432-1343"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Classification","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320274","display_name":"University of East Anglia","ror":"https://ror.org/026k5mg93"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2737180220.pdf","grobid_xml":"https://content.openalex.org/works/W2737180220.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1834060250","https://openalex.org/W1967454590","https://openalex.org/W1974452403","https://openalex.org/W1991581005","https://openalex.org/W1992296962","https://openalex.org/W2013951784","https://openalex.org/W2022221380","https://openalex.org/W2041346050","https://openalex.org/W2041866406","https://openalex.org/W2078109763","https://openalex.org/W2093777580","https://openalex.org/W2126946913","https://openalex.org/W2286429956","https://openalex.org/W2301157271","https://openalex.org/W2584536054","https://openalex.org/W2914340152"],"related_works":["https://openalex.org/W2962866177","https://openalex.org/W2950235462","https://openalex.org/W3082977496","https://openalex.org/W3106915313","https://openalex.org/W180559377","https://openalex.org/W2765484734","https://openalex.org/W2950833721","https://openalex.org/W1993195769","https://openalex.org/W3208851320","https://openalex.org/W3088209886","https://openalex.org/W2863520273","https://openalex.org/W2144144677","https://openalex.org/W3134261402","https://openalex.org/W2008624417","https://openalex.org/W3037575406","https://openalex.org/W2045875391","https://openalex.org/W2561058488","https://openalex.org/W2564532582","https://openalex.org/W2034145232","https://openalex.org/W2914009758"],"abstract_inverted_index":{"Three-way":[0],"dissimilarities":[1,7,52],"are":[2,53,85],"a":[3,118,167,190,193,197,210,221],"generalization":[4,119],"of":[5,16,50,91,120,125,170,212,246],"(two-way)":[6,122],"which":[8,58,75],"can":[9,46,114,145,178,217],"be":[10,115,146,179,218,230],"used":[11,34],"to":[12,161],"indicate":[13],"the":[14,82,121,153,203,244],"lack":[15],"homogeneity":[17],"or":[18,182,192,215],"resemblance":[19],"between":[20],"any":[21],"three":[22],"objects.":[23],"Such":[24],"maps":[25,74,99],"have":[26,32],"applications":[27],"in":[28,35,232],"cluster":[29],"analysis":[30],"and":[31,40,56,127,135,138,143,236],"been":[33],"areas":[36],"such":[37,51,98],"as":[38,117,132],"psychology":[39],"phylogenetics,":[41],"where":[42,80],"three-way":[43,54,73,100,109,136,140,186],"data":[44],"tables":[45],"arise.":[47],"Special":[48],"examples":[49],"tree-metrics":[55,137],"ultrametrics,":[57,139],"arise":[59,76],"from":[60,77],"leaf-labelled":[61,78],"trees":[62,79,214],"with":[63,133],"edges":[64],"labelled":[65,86],"by":[66,87,164,220],"positive":[67],"real":[68],"numbers.":[69],"Here":[70],"we":[71,96,106],"consider":[72],"instead":[81],"interior":[83],"vertices":[84],"an":[88,184],"arbitrary":[89,185],"set":[90,211],"values.":[92],"For":[93],"unrooted":[94,154],"trees,":[95,105],"call":[97,107],"symbolic":[101,110,123,141,187,194],"tree-maps;":[102],"for":[103,166,207,238],"rooted":[104],"them":[108],"ultrametrics":[111,124,144],"since":[112],"they":[113],"considered":[116],"Bocker":[126],"Dress.":[128],"We":[129,173,224],"show":[130,175],"that,":[131],"two-":[134],"tree-maps":[142],"characterized":[147],"via":[148],"certain":[149,168],"k-point":[150],"conditions.":[151],"In":[152],"case,":[155],"our":[156,227],"characterization":[157],"is":[158,189],"mathematically":[159],"equivalent":[160],"one":[162],"presented":[163],"Gurvich":[165],"class":[169],"edge-labelled":[171],"hypergraphs.":[172],"also":[174],"that":[176,200,226],"it":[177],"decided":[180],"whether":[181],"not":[183],"map":[188],"tree-map":[191],"ultrametric":[195],"using":[196],"triplet-based":[198],"approach":[199],"relies":[201],"on":[202],"so-called":[204],"BUILD":[205],"algorithm":[206],"deciding":[208],"when":[209],"3-leaved":[213],"triplets":[216],"displayed":[219],"single":[222],"tree.":[223],"envisage":[225],"results":[228],"will":[229],"useful":[231],"developing":[233],"new":[234],"approaches":[235],"algorithms":[237],"understanding":[239],"3-way":[240],"data,":[241],"especially":[242],"within":[243],"area":[245],"phylogenetics.":[247]},"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}