{"id":"https://openalex.org/W2972443286","doi":"https://doi.org/10.1007/s11222-020-09932-y","title":"Metrics and barycenters for point pattern data","display_name":"Metrics and barycenters for point pattern data","publication_year":2020,"publication_date":"2020-02-24","ids":{"openalex":"https://openalex.org/W2972443286","doi":"https://doi.org/10.1007/s11222-020-09932-y","mag":"2972443286"},"language":"en","primary_location":{"id":"doi:10.1007/s11222-020-09932-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11222-020-09932-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11222-020-09932-y.pdf","source":{"id":"https://openalex.org/S5437875","display_name":"Statistics and Computing","issn_l":"0960-3174","issn":["0960-3174","1573-1375"],"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":"Statistics and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11222-020-09932-y.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017879408","display_name":"Raoul M\u00fcller","orcid":null},"institutions":[{"id":"https://openalex.org/I74656192","display_name":"University of G\u00f6ttingen","ror":"https://ror.org/01y9bpm73","country_code":"DE","type":"education","lineage":["https://openalex.org/I74656192"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Raoul M\u00fcller","raw_affiliation_strings":["Institute for Mathematical Stochastics, University of G\u00f6ttingen, 37077, G\u00f6ttingen, Germany","Institute for Mathematical Stochastics , University of G\u00f6ttingen , Gottingen , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Mathematical Stochastics, University of G\u00f6ttingen, 37077, G\u00f6ttingen, Germany","institution_ids":["https://openalex.org/I74656192"]},{"raw_affiliation_string":"Institute for Mathematical Stochastics , University of G\u00f6ttingen , Gottingen , Germany","institution_ids":["https://openalex.org/I74656192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049043391","display_name":"Dominic Schuhmacher","orcid":"https://orcid.org/0000-0001-7079-6313"},"institutions":[{"id":"https://openalex.org/I74656192","display_name":"University of G\u00f6ttingen","ror":"https://ror.org/01y9bpm73","country_code":"DE","type":"education","lineage":["https://openalex.org/I74656192"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Dominic Schuhmacher","raw_affiliation_strings":["Institute for Mathematical Stochastics, University of G\u00f6ttingen, 37077, G\u00f6ttingen, Germany","Institute for Mathematical Stochastics , University of G\u00f6ttingen , Gottingen , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Mathematical Stochastics, University of G\u00f6ttingen, 37077, G\u00f6ttingen, Germany","institution_ids":["https://openalex.org/I74656192"]},{"raw_affiliation_string":"Institute for Mathematical Stochastics , University of G\u00f6ttingen , Gottingen , Germany","institution_ids":["https://openalex.org/I74656192"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103185957","display_name":"Jorge Mateu","orcid":"https://orcid.org/0000-0002-2868-7604"},"institutions":[{"id":"https://openalex.org/I10902133","display_name":"Universitat Jaume I","ror":"https://ror.org/02ws1xc11","country_code":"ES","type":"education","lineage":["https://openalex.org/I10902133"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jorge Mateu","raw_affiliation_strings":["Department of Mathematics, University Jaume I, 12071, Castell\u00f3n, Spain","Department of Mathematics, University Jaume I, Castell\u00f3n, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University Jaume I, 12071, Castell\u00f3n, Spain","institution_ids":["https://openalex.org/I10902133"]},{"raw_affiliation_string":"Department of Mathematics, University Jaume I, Castell\u00f3n, Spain","institution_ids":["https://openalex.org/I10902133"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5017879408"],"corresponding_institution_ids":["https://openalex.org/I74656192"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":{"value":2890,"currency":"USD","value_usd":2890},"fwci":0.2821,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.42310387,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"30","issue":"4","first_page":"953","last_page":"972"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9945999979972839,"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/T12417","display_name":"Morphological variations and asymmetry","score":0.9927999973297119,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.5858126282691956},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.5532971620559692},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.537239134311676},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.516771674156189},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.5080175399780273},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4967828392982483},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.49336472153663635},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4667993187904358},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4483283758163452},{"id":"https://openalex.org/keywords/statistical-inference","display_name":"Statistical inference","score":0.4218939542770386},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.41088971495628357},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3735818862915039},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3321036994457245},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.13573956489562988},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11522111296653748}],"concepts":[{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.5858126282691956},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.5532971620559692},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.537239134311676},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.516771674156189},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.5080175399780273},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4967828392982483},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.49336472153663635},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4667993187904358},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4483283758163452},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.4218939542770386},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.41088971495628357},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3735818862915039},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3321036994457245},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.13573956489562988},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11522111296653748},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s11222-020-09932-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11222-020-09932-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11222-020-09932-y.pdf","source":{"id":"https://openalex.org/S5437875","display_name":"Statistics and Computing","issn_l":"0960-3174","issn":["0960-3174","1573-1375"],"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":"Statistics and Computing","raw_type":"journal-article"},{"id":"pmh:oai:repositori.uji.es:10234/190063","is_oa":false,"landing_page_url":"http://hdl.handle.net/10234/190063","pdf_url":null,"source":{"id":"https://openalex.org/S4306400303","display_name":"Repositori UJI (Universitat Jaume I)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I10902133","host_organization_name":"Universitat Jaume I","host_organization_lineage":["https://openalex.org/I10902133"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"mag:2972443286","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1909.07266","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:publications.goettingen-research-online.de:2/71248","is_oa":true,"landing_page_url":"https://resolver.sub.uni-goettingen.de/purl?gro-2/71248","pdf_url":null,"source":{"id":"https://openalex.org/S4306401634","display_name":"GoeScholar  The Publication Server of the Georg-August-Universit\u00e4t G\u00f6ttingen (Georg-August-Universit\u00e4t G\u00f6ttingen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210122495","host_organization_name":"Asklepios Klinik St. Georg","host_organization_lineage":["https://openalex.org/I4210122495"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"journal_article"},{"id":"doi:10.48550/arxiv.1909.07266","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1909.07266","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":"Preprint"}],"best_oa_location":{"id":"doi:10.1007/s11222-020-09932-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11222-020-09932-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11222-020-09932-y.pdf","source":{"id":"https://openalex.org/S5437875","display_name":"Statistics and Computing","issn_l":"0960-3174","issn":["0960-3174","1573-1375"],"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":"Statistics and Computing","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.8100000023841858,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G1922752267","display_name":null,"funder_award_id":"DFG RTG 2088","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G3371003963","display_name":null,"funder_award_id":"MTM201678917-R","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G4984910068","display_name":null,"funder_award_id":"RTG2088","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G611313543","display_name":null,"funder_award_id":"GRK\u00a02088","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2972443286.pdf","grobid_xml":"https://content.openalex.org/works/W2972443286.grobid-xml"},"referenced_works_count":49,"referenced_works":["https://openalex.org/W83403172","https://openalex.org/W1503896428","https://openalex.org/W1535106372","https://openalex.org/W1629559917","https://openalex.org/W1968333723","https://openalex.org/W2009070933","https://openalex.org/W2013445852","https://openalex.org/W2019162816","https://openalex.org/W2033574929","https://openalex.org/W2102750402","https://openalex.org/W2107696819","https://openalex.org/W2122505562","https://openalex.org/W2126885789","https://openalex.org/W2128123518","https://openalex.org/W2217701558","https://openalex.org/W2222512263","https://openalex.org/W2246915724","https://openalex.org/W2266946488","https://openalex.org/W2296650473","https://openalex.org/W2298250094","https://openalex.org/W2337241360","https://openalex.org/W2550548986","https://openalex.org/W2582743722","https://openalex.org/W2608882164","https://openalex.org/W2724892359","https://openalex.org/W2743430388","https://openalex.org/W2743695096","https://openalex.org/W2744110160","https://openalex.org/W2764290944","https://openalex.org/W2794923930","https://openalex.org/W2799837476","https://openalex.org/W2809783152","https://openalex.org/W2963319702","https://openalex.org/W2963448920","https://openalex.org/W2966168789","https://openalex.org/W2968258146","https://openalex.org/W2982359386","https://openalex.org/W2990312679","https://openalex.org/W2995524248","https://openalex.org/W3047066292","https://openalex.org/W3093545757","https://openalex.org/W3101366889","https://openalex.org/W3102246635","https://openalex.org/W3103801447","https://openalex.org/W3145128584","https://openalex.org/W4250310729","https://openalex.org/W4291236916","https://openalex.org/W4399588944","https://openalex.org/W6601365666"],"related_works":["https://openalex.org/W3008025834","https://openalex.org/W2038102631","https://openalex.org/W1931096776","https://openalex.org/W3020649082","https://openalex.org/W2189338950","https://openalex.org/W3035954658","https://openalex.org/W2938110878","https://openalex.org/W2136783219","https://openalex.org/W3038086609","https://openalex.org/W3133311760","https://openalex.org/W2903087677","https://openalex.org/W3034788693","https://openalex.org/W3028017209","https://openalex.org/W2404339789","https://openalex.org/W2979677937","https://openalex.org/W1594985570","https://openalex.org/W2951393143","https://openalex.org/W2998578697","https://openalex.org/W3127874251","https://openalex.org/W2739573680"],"abstract_inverted_index":{"Abstract":[0],"We":[1,60,116],"introduce":[2],"the":[3,6,30,35,108],"transport\u2013transform":[4,8],"and":[5,34,37,71,77,127],"relative":[7],"metrics":[9],"between":[10],"finite":[11],"point":[12,25,96,154],"patterns":[13,97],"on":[14,47,98,128],"a":[15,20,62,68,80,87,129,143],"general":[16,88],"space,":[17],"which":[18],"provide":[19],"unified":[21],"framework":[22],"for":[23,106,111],"earlier":[24],"pattern":[26,155],"metrics,":[27],"in":[28,67,79,124,149],"particular":[29],"generalized":[31],"spike":[32],"time":[33],"normalized":[36],"unnormalized":[38],"optimal":[39],"subpattern":[40],"assignment":[41],"metrics.":[42,59],"Our":[43,140],"main":[44],"focus":[45],"is":[46,72,114,142],"barycenters,":[48],"i.e.,":[49],"minimizers":[50],"of":[51,122,152],"aq-th-order":[52],"Fr\u00e9chet":[53],"functional":[54],"with":[55],"respect":[56],"to":[57,74,95,119],"these":[58],"present":[61,117],"heuristic":[63],"algorithm":[64,84,105],"that":[65,91,133],"terminates":[66],"local":[69],"minimum":[70],"shown":[73],"be":[75,93],"fast":[76],"reliable":[78],"simulation":[81],"study.":[82],"The":[83],"serves":[85],"as":[86,136],"plug-in":[89],"method":[90],"can":[92],"applied":[94],"any":[99],"state":[100],"space":[101,126],"where":[102],"an":[103],"appropriate":[104],"solving":[107],"location":[109],"problem":[110],"individual":[112],"points":[113],"available.":[115],"applications":[118],"geocoded":[120],"data":[121],"crimes":[123],"Euclidean":[125],"street":[130],"network,":[131],"illustrating":[132],"barycenters":[134],"serve":[135],"informative":[137],"summary":[138],"statistics.":[139],"work":[141],"first":[144],"step":[145],"toward":[146],"statistical":[147],"inference":[148],"covariate-based":[150],"models":[151],"repeated":[153],"observations.":[156]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
