{"id":"https://openalex.org/W3046985715","doi":"https://doi.org/10.1080/24694452.2020.1774350","title":"Scalable GWR: A Linear-Time Algorithm for Large-Scale Geographically Weighted Regression with Polynomial Kernels","display_name":"Scalable GWR: A Linear-Time Algorithm for Large-Scale Geographically Weighted Regression with Polynomial Kernels","publication_year":2020,"publication_date":"2020-08-03","ids":{"openalex":"https://openalex.org/W3046985715","doi":"https://doi.org/10.1080/24694452.2020.1774350","mag":"3046985715"},"language":"en","primary_location":{"id":"doi:10.1080/24694452.2020.1774350","doi":"https://doi.org/10.1080/24694452.2020.1774350","is_oa":true,"landing_page_url":"https://doi.org/10.1080/24694452.2020.1774350","pdf_url":"https://www.tandfonline.com/doi/pdf/10.1080/24694452.2020.1774350?needAccess=true","source":{"id":"https://openalex.org/S2764498735","display_name":"Annals of the American Association of Geographers","issn_l":"2469-4452","issn":["2469-4452","2469-4460"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"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":"Annals of the American Association of Geographers","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.tandfonline.com/doi/pdf/10.1080/24694452.2020.1774350?needAccess=true","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039934688","display_name":"Daisuke Murakami","orcid":"https://orcid.org/0000-0002-9544-9542","observed_orcids":["https://orcid.org/0000-0002-9544-9542"]},"institutions":[{"id":"https://openalex.org/I4210134673","display_name":"The Institute of Statistical Mathematics","ror":"https://ror.org/03jcejr58","country_code":"JP","type":"facility","lineage":["https://openalex.org/I1319490839","https://openalex.org/I4210134673","https://openalex.org/I4210158934"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Daisuke Murakami","raw_affiliation_strings":["Department of Statistical Modeling, The Institute of Statistical Mathematics"],"raw_orcid":"https://orcid.org/0000-0002-9544-9542","affiliations":[{"raw_affiliation_string":"Department of Statistical Modeling, The Institute of Statistical Mathematics","institution_ids":["https://openalex.org/I4210134673"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073788639","display_name":"Narumasa Tsutsumida","orcid":"https://orcid.org/0000-0002-6333-0301","observed_orcids":["https://orcid.org/0000-0002-6333-0301"]},"institutions":[{"id":"https://openalex.org/I22299242","display_name":"Kyoto University","ror":"https://ror.org/02kpeqv85","country_code":"JP","type":"education","lineage":["https://openalex.org/I22299242"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Narumasa Tsutsumida","raw_affiliation_strings":["Graduate School of Global Environmental Studies, Kyoto University"],"raw_orcid":"https://orcid.org/0000-0002-6333-0301","affiliations":[{"raw_affiliation_string":"Graduate School of Global Environmental Studies, Kyoto University","institution_ids":["https://openalex.org/I22299242"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022824333","display_name":"Takahiro Yoshida","orcid":"https://orcid.org/0000-0001-8741-5345","observed_orcids":["https://orcid.org/0000-0001-8741-5345"]},"institutions":[{"id":"https://openalex.org/I200202764","display_name":"National Institute for Environmental Studies","ror":"https://ror.org/02hw5fp67","country_code":"JP","type":"education","lineage":["https://openalex.org/I200202764"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Takahiro Yoshida","raw_affiliation_strings":["Center for Global Environmental Research, National Institute for Environmental Studies"],"raw_orcid":"https://orcid.org/0000-0001-8741-5345","affiliations":[{"raw_affiliation_string":"Center for Global Environmental Research, National Institute for Environmental Studies","institution_ids":["https://openalex.org/I200202764"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060059803","display_name":"Tomoki Nakaya","orcid":"https://orcid.org/0000-0002-3827-1012","observed_orcids":["https://orcid.org/0000-0002-3827-1012"]},"institutions":[{"id":"https://openalex.org/I22299242","display_name":"Kyoto University","ror":"https://ror.org/02kpeqv85","country_code":"JP","type":"education","lineage":["https://openalex.org/I22299242"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Tomoki Nakaya","raw_affiliation_strings":["Graduate School of Global Environmental Studies, Kyoto University"],"raw_orcid":"https://orcid.org/0000-0002-3827-1012","affiliations":[{"raw_affiliation_string":"Graduate School of Global Environmental Studies, Kyoto University","institution_ids":["https://openalex.org/I22299242"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023127879","display_name":"Binbin Lu","orcid":"https://orcid.org/0000-0001-7847-7560","observed_orcids":["https://orcid.org/0000-0001-7847-7560"]},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Binbin Lu","raw_affiliation_strings":["School of Remote Sensing and Information Engineering, Wuhan University"],"raw_orcid":"https://orcid.org/0000-0001-7847-7560","affiliations":[{"raw_affiliation_string":"School of Remote Sensing and Information Engineering, Wuhan University","institution_ids":["https://openalex.org/I37461747"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.823,"has_fulltext":true,"cited_by_count":53,"citation_normalized_percentile":{"value":0.96963293,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"111","issue":"2","first_page":"459","last_page":"480"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11911","display_name":"Spatial and Panel Data Analysis","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11911","display_name":"Spatial and Panel Data Analysis","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T14509","display_name":"demographic modeling and climate adaptation","score":0.0,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12343","display_name":"Geography Education and Pedagogy","score":0.0,"subfield":{"id":"https://openalex.org/subfields/3305","display_name":"Geography, Planning and Development"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/geographically-weighted-regression","display_name":"geographically weighted regression","score":0.9929999709129333},{"id":"https://openalex.org/keywords/polynomial-kernel","display_name":"polynomial kernel","score":0.9750000238418579},{"id":"https://openalex.org/keywords/leave-one-out-cross-validation","display_name":"leave-one-out cross-validation","score":0.9959999918937683},{"id":"https://openalex.org/keywords/empirical-bayes","display_name":"empirical Bayes","score":0.8999999761581421},{"id":"https://openalex.org/keywords/computational-efficiency","display_name":"computational efficiency","score":0.7730000019073486},{"id":"https://openalex.org/keywords/income-analysis","display_name":"income analysis","score":0.5669999718666077},{"id":"https://openalex.org/keywords/big-data","display_name":"big data","score":0.5049999952316284}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.670515775680542},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6476165056228638},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6103527545928955},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4533580541610718},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.45159029960632324},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.44320714473724365},{"id":"https://openalex.org/C48921125","wikidata":"https://www.wikidata.org/wiki/Q10861030","display_name":"Linear regression","level":2,"score":0.41311293840408325},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2956202030181885},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.25268036127090454},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.15376001596450806},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.08323746919631958}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1080/24694452.2020.1774350","doi":"https://doi.org/10.1080/24694452.2020.1774350","is_oa":true,"landing_page_url":"https://doi.org/10.1080/24694452.2020.1774350","pdf_url":"https://www.tandfonline.com/doi/pdf/10.1080/24694452.2020.1774350?needAccess=true","source":{"id":"https://openalex.org/S2764498735","display_name":"Annals of the American Association of Geographers","issn_l":"2469-4452","issn":["2469-4452","2469-4460"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"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":"Annals of the American Association of Geographers","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1905.00266","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1905.00266","pdf_url":"https://arxiv.org/pdf/1905.00266","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,"listed_in":[],"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":null,"raw_type":"text"},{"id":"pmh:oai:RePEc:taf:raagxx:v:111:y:2020:i:2:p:459-480","doi":null,"is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1080/24694452.2020.1774350","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,"listed_in":[],"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.1905.00266","doi":"https://doi.org/10.48550/arxiv.1905.00266","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1905.00266","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,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.1080/24694452.2020.1774350","doi":"https://doi.org/10.1080/24694452.2020.1774350","is_oa":true,"landing_page_url":"https://doi.org/10.1080/24694452.2020.1774350","pdf_url":"https://www.tandfonline.com/doi/pdf/10.1080/24694452.2020.1774350?needAccess=true","source":{"id":"https://openalex.org/S2764498735","display_name":"Annals of the American Association of Geographers","issn_l":"2469-4452","issn":["2469-4452","2469-4460"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"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":"Annals of the American Association of Geographers","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1016183770","display_name":null,"funder_award_id":"41871287","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2152131095","display_name":"Challenges and new developments to the most important issues in spatial econometrics","funder_award_id":"18H03628","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G3959840547","display_name":"Spatial regression modeling estimating a wide variety of effects from diverse data","funder_award_id":"20K13261","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G4704776589","display_name":"Development of Methodology for Geographic Crime Prediction -Establishment of academic infrastructure and system development through interdisciplinary research and industry-academia collaboration","funder_award_id":"17H02046","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G4772630408","display_name":"Developmnent and Application of next-generation tool box for analyzing temporal-spatial information","funder_award_id":"16H01830","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G4846050025","display_name":"Theoretical and empirical studies on spatio-temporal agglomeration of economic activities","funder_award_id":"18H01556","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G7516027415","display_name":null,"funder_award_id":"U1833201","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G828660308","display_name":null,"funder_award_id":"41725006","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320323628","display_name":"Support Center for Advanced Telecommunications Technology Research Foundation","ror":"https://ror.org/03x526f83"},{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3046985715.pdf","grobid_xml":"https://content.openalex.org/works/W3046985715.grobid-xml"},"referenced_works_count":58,"referenced_works":["https://openalex.org/W247501010","https://openalex.org/W585085135","https://openalex.org/W1250261183","https://openalex.org/W1524392826","https://openalex.org/W1549544876","https://openalex.org/W1599043334","https://openalex.org/W1663973292","https://openalex.org/W1773028378","https://openalex.org/W1898904249","https://openalex.org/W1976840258","https://openalex.org/W1980398988","https://openalex.org/W1984892485","https://openalex.org/W2004807582","https://openalex.org/W2022664803","https://openalex.org/W2041890084","https://openalex.org/W2045066934","https://openalex.org/W2052077920","https://openalex.org/W2061320421","https://openalex.org/W2064385888","https://openalex.org/W2066986995","https://openalex.org/W2083336903","https://openalex.org/W2084005892","https://openalex.org/W2084032127","https://openalex.org/W2131421516","https://openalex.org/W2134006231","https://openalex.org/W2143022286","https://openalex.org/W2144898279","https://openalex.org/W2147279463","https://openalex.org/W2148323323","https://openalex.org/W2156378058","https://openalex.org/W2160061095","https://openalex.org/W2496675188","https://openalex.org/W2557979057","https://openalex.org/W2559688945","https://openalex.org/W2562729256","https://openalex.org/W2573715514","https://openalex.org/W2599875474","https://openalex.org/W2605661896","https://openalex.org/W2747207142","https://openalex.org/W2767465154","https://openalex.org/W2771875082","https://openalex.org/W2792683512","https://openalex.org/W2795443545","https://openalex.org/W2796128890","https://openalex.org/W2799211855","https://openalex.org/W2803271468","https://openalex.org/W2883124148","https://openalex.org/W2894189093","https://openalex.org/W2901615696","https://openalex.org/W2913666622","https://openalex.org/W2921548915","https://openalex.org/W2943910047","https://openalex.org/W2948613401","https://openalex.org/W2963022999","https://openalex.org/W2963599152","https://openalex.org/W2993176323","https://openalex.org/W3000508506","https://openalex.org/W4206379942"],"related_works":["https://openalex.org/W6925364111","https://openalex.org/W6939658077","https://openalex.org/W2901615696","https://openalex.org/W4388976969","https://openalex.org/W4301172683","https://openalex.org/W7028968974","https://openalex.org/W4416768806","https://openalex.org/W4385202189","https://openalex.org/W7097095369","https://openalex.org/W4386137992"],"abstract_inverted_index":{"Although":[0],"a":[1,26,45,63,164,174],"number":[2],"of":[3,17,59,65,157],"studies":[4],"have":[5],"developed":[6],"fast":[7],"geographically":[8],"weighted":[9],"regression":[10],"(GWR)":[11],"algorithms":[12],"for":[13,28,49,180],"large":[14,50],"samples,":[15],"none":[16],"them":[18],"has":[19],"achieved":[20],"linear-time":[21],"estimation,":[22],"which":[23,82],"is":[24,56,83,139,182,191],"considered":[25],"requisite":[27],"big":[29],"data":[30,51],"analysis":[31],"in":[32,88,155,184,198],"machine":[33],"learning,":[34],"geostatistics,":[35],"and":[36,68,160,196],"related":[37],"domains.":[38],"Against":[39],"this":[40,42,113],"backdrop,":[41],"study":[43],"proposes":[44],"scalable":[46],"GWR":[47,99,145,154],"(ScaGWR)":[48],"sets.":[52],"The":[53,178,189],"key":[54],"improvement":[55],"the":[57,60,66,74,79,84,97,109,115,127,143,149,152,185],"calibration":[58],"model":[61],"through":[62],"precompression":[64,92],"matrices":[67],"vectors":[69],"whose":[70],"size":[71],"depends":[72],"on":[73],"sample":[75,110],"size,":[76],"prior":[77],"to":[78,95,173],"leave-one-out":[80],"cross-validation,":[81],"heaviest":[85],"computational":[86,161],"step":[87],"conventional":[89,144,153],"GWR.":[90],"This":[91],"allows":[93],"us":[94],"run":[96],"proposed":[98],"extension":[100],"so":[101],"that":[102,138],"its":[103],"computation":[104],"time":[105],"increases":[106],"linearly":[107],"with":[108,120,151],"size.":[111],"With":[112],"improvement,":[114],"ScaGWR":[116,128,150,181],"can":[117,130],"be":[118,131],"calibrated":[119],"1":[121],"million":[122],"observations":[123],"without":[124],"parallelization.":[125],"Moreover,":[126],"estimator":[129,137],"regarded":[132],"as":[133],"an":[134],"empirical":[135],"Bayesian":[136],"more":[140],"stable":[141],"than":[142],"estimator.":[146],"We":[147],"compare":[148],"terms":[156],"estimation":[158],"accuracy":[159],"efficiency":[162],"using":[163],"Monte":[165],"Carlo":[166],"simulation.":[167],"Then,":[168],"we":[169],"apply":[170],"these":[171],"methods":[172],"U.S.":[175],"income":[176],"analysis.":[177],"code":[179,190,195],"available":[183],"R":[186,200],"package":[187],"scgwr.":[188],"embedded":[192],"into":[193],"C++":[194],"implemented":[197],"another":[199],"package,":[201],"GWmodel.":[202]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":2}],"updated_date":"2026-11-03T10:50:19.383937","created_date":"2020-08-10T00:00:00"}
