{"id":"https://openalex.org/W4402954270","doi":"https://doi.org/10.48550/arxiv.2409.01010","title":"Fitting trees to $\\ell_1$-hyperbolic distances","display_name":"Fitting trees to $\\ell_1$-hyperbolic distances","publication_year":2024,"publication_date":"2024-09-02","ids":{"openalex":"https://openalex.org/W4402954270","doi":"https://doi.org/10.48550/arxiv.2409.01010"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2409.01010","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2409.01010","pdf_url":"https://arxiv.org/pdf/2409.01010","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2409.01010","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5107649387","display_name":"Joon-Hyeok Yim","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yim, Joon-Hyeok","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5042502878","display_name":"Anna C. Gilbert","orcid":"https://orcid.org/0000-0002-9627-9274"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gilbert, Anna C.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9861000180244446,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9861000180244446,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9684000015258789,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.9668999910354614,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49070537090301514},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.4139788746833801},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3391683101654053},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.3296216130256653}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49070537090301514},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.4139788746833801},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3391683101654053},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.3296216130256653}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2409.01010","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2409.01010","pdf_url":"https://arxiv.org/pdf/2409.01010","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"doi:10.48550/arxiv.2409.01010","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2409.01010","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2409.01010","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2409.01010","pdf_url":"https://arxiv.org/pdf/2409.01010","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4402954270.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885"],"abstract_inverted_index":{"Building":[0],"trees":[1],"to":[2,5,120,127,214],"represent":[3],"or":[4],"fit":[6,119],"distances":[7],"is":[8,177,200,269],"a":[9,46,89,136,156,259],"critical":[10],"component":[11],"of":[12,26,30,56,81,91,98,105,112,115,135,140,153,173,182,186,251,264],"phylogenetic":[13],"analysis,":[14],"metric":[15,40],"embeddings,":[16],"approximation":[17],"algorithms,":[18,229],"geometric":[19,60,240],"graph":[20,241],"neural":[21,242],"nets,":[22],"and":[23,59,78,100,196,209,217,225,239],"the":[24,31,53,65,71,74,79,102,109,113,116,121,129,141,148,170,174,183,187],"analysis":[25,55,238,263],"hierarchical":[27,236],"data.":[28],"Much":[29],"previous":[32],"algorithmic":[33],"work,":[34],"however,":[35],"has":[36,205],"focused":[37],"on":[38],"generic":[39],"spaces":[41],"(i.e.,":[42,190],"those":[43,250],"with":[44,108],"no":[45],"priori":[47],"constraints).":[48],"Leveraging":[49],"several":[50],"ideas":[51],"from":[52],"mathematical":[54],"hyperbolic":[57],"geometry":[58],"group":[61],"theory,":[62],"we":[63,87,145,221],"study":[64],"tree":[66,82,118,150,227,247],"fitting":[67,151,228],"problem":[68],"as":[69,155,212],"finding":[70],"relation":[72],"between":[73],"hyperbolicity":[75,92,131,142,188],"(ultrametricity)":[76,132],"vector":[77,90,107,189],"error":[80,172],"(ultrametric)":[83,93],"embedding.":[84],"That":[85],"is,":[86],"define":[88,128],"values":[94],"over":[95],"all":[96],"triples":[97],"points":[99],"compare":[101],"$\\ell_p$":[103],"norms":[104],"this":[106,198,203],"$\\ell_q$":[110],"norm":[111,139,185],"distortion":[114],"best":[117],"distances.":[122],"This":[123],"formulation":[124],"allows":[125],"us":[126],"average":[130],"in":[133,180],"terms":[134,181],"normalized":[137],"$\\ell_1$":[138,171,184],"vector.":[143],"Furthermore,":[144,202],"can":[146],"interpret":[147],"classical":[149],"result":[152,199,216],"Gromov":[154],"$p":[157,191],"=":[158,160,192,194],"q":[159,193],"\\infty$":[161],"result.":[162],"We":[163],"present":[164],"an":[165],"algorithm":[166,204],"HCCRootedTreeFit":[167,224],"such":[168],"that":[169,197,230,258],"output":[175],"embedding":[176],"analytically":[178],"bounded":[179],"1$)":[195],"tight.":[201],"significantly":[206],"different":[207,246],"theoretical":[208],"empirical":[210],"performance":[211],"compared":[213],"Gromov's":[215],"related":[218,226],"algorithms.":[219],"Finally,":[220],"show":[222],"using":[223],"supposedly":[231],"standard":[232,266],"data":[233,237,255,267],"sets":[234,268],"for":[235],"networks":[243],"have":[244],"radically":[245],"fits":[248],"than":[249],"synthetic,":[252],"truly":[253],"tree-like":[254],"sets,":[256],"suggesting":[257],"much":[260],"more":[261],"refined":[262],"these":[265],"called":[270],"for.":[271]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}