{"id":"https://openalex.org/W4386137992","doi":"https://doi.org/10.1080/13658816.2023.2246154","title":"Gradient-based optimization for multi-scale geographically weighted regression","display_name":"Gradient-based optimization for multi-scale geographically weighted regression","publication_year":2023,"publication_date":"2023-08-24","ids":{"openalex":"https://openalex.org/W4386137992","doi":"https://doi.org/10.1080/13658816.2023.2246154"},"language":"en","primary_location":{"id":"doi:10.1080/13658816.2023.2246154","doi":"https://doi.org/10.1080/13658816.2023.2246154","is_oa":false,"landing_page_url":"https://doi.org/10.1080/13658816.2023.2246154","pdf_url":null,"source":{"id":"https://openalex.org/S4210181446","display_name":"International Journal of Geographical Information Systems","issn_l":"0269-3798","issn":["0269-3798","1362-3087"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["dongbi-b","poland-100"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Geographical Information Science","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Xiaodan Zhou","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1292842697","display_name":"Environmental Systems Research Institute (United States)","ror":"https://ror.org/0428exr50","country_code":"US","type":"company","lineage":["https://openalex.org/I1292842697"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xiaodan Zhou","raw_affiliation_strings":["ESRI Inc, Redlands, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ESRI Inc, Redlands, CA, USA","institution_ids":["https://openalex.org/I1292842697"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009808819","display_name":"Renato Assun\u00e7\u00e3o","orcid":"https://orcid.org/0000-0001-7442-9166","observed_orcids":["https://orcid.org/0000-0001-7442-9166"]},"institutions":[{"id":"https://openalex.org/I110200422","display_name":"Universidade Federal de Minas Gerais","ror":"https://ror.org/0176yjw32","country_code":"BR","type":"education","lineage":["https://openalex.org/I110200422"]},{"id":"https://openalex.org/I1292842697","display_name":"Environmental Systems Research Institute (United States)","ror":"https://ror.org/0428exr50","country_code":"US","type":"company","lineage":["https://openalex.org/I1292842697"]}],"countries":["BR","US"],"is_corresponding":true,"raw_author_name":"Renato Assun\u00e7\u00e3o","raw_affiliation_strings":["Departamento de Ci\u00eancia da Computa\u00e7\u00e3o, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil","ESRI Inc, Redlands, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Ci\u00eancia da Computa\u00e7\u00e3o, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil","institution_ids":["https://openalex.org/I110200422"]},{"raw_affiliation_string":"ESRI Inc, Redlands, CA, USA","institution_ids":["https://openalex.org/I1292842697"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112411529","display_name":"Hu Shao","orcid":"https://orcid.org/0000-0003-3852-3176","observed_orcids":["https://orcid.org/0000-0003-3852-3176"]},"institutions":[{"id":"https://openalex.org/I1292842697","display_name":"Environmental Systems Research Institute (United States)","ror":"https://ror.org/0428exr50","country_code":"US","type":"company","lineage":["https://openalex.org/I1292842697"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hu Shao","raw_affiliation_strings":["ESRI Inc, Redlands, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ESRI Inc, Redlands, CA, USA","institution_ids":["https://openalex.org/I1292842697"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101195190","display_name":"Cheng-Chia Huang","orcid":"https://orcid.org/0000-0002-6016-4299","observed_orcids":["https://orcid.org/0000-0002-6016-4299"]},"institutions":[{"id":"https://openalex.org/I1292842697","display_name":"Environmental Systems Research Institute (United States)","ror":"https://ror.org/0428exr50","country_code":"US","type":"company","lineage":["https://openalex.org/I1292842697"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Cheng-Chia Huang","raw_affiliation_strings":["ESRI Inc, Redlands, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ESRI Inc, Redlands, CA, USA","institution_ids":["https://openalex.org/I1292842697"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068960918","display_name":"Mark V. Janikas","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1292842697","display_name":"Environmental Systems Research Institute (United States)","ror":"https://ror.org/0428exr50","country_code":"US","type":"company","lineage":["https://openalex.org/I1292842697"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mark Janikas","raw_affiliation_strings":["ESRI Inc, Redlands, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ESRI Inc, Redlands, CA, USA","institution_ids":["https://openalex.org/I1292842697"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072551270","display_name":"Hanna Asefaw","orcid":"https://orcid.org/0000-0002-4873-4754","observed_orcids":["https://orcid.org/0000-0002-4873-4754"]},"institutions":[{"id":"https://openalex.org/I1292842697","display_name":"Environmental Systems Research Institute (United States)","ror":"https://ror.org/0428exr50","country_code":"US","type":"company","lineage":["https://openalex.org/I1292842697"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hanna Asefaw","raw_affiliation_strings":["ESRI Inc, Redlands, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ESRI Inc, Redlands, CA, USA","institution_ids":["https://openalex.org/I1292842697"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5009808819"],"corresponding_institution_ids":["https://openalex.org/I110200422","https://openalex.org/I1292842697"],"apc_list":null,"apc_paid":null,"fwci":2.7512,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.90631027,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"37","issue":"10","first_page":"2101","last_page":"2128"},"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/T10770","display_name":"Soil Geostatistics and Mapping","score":0.0,"subfield":{"id":"https://openalex.org/subfields/1111","display_name":"Soil Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life 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/multiscale-geographically-weighted-regression","display_name":"multiscale geographically weighted regression","score":0.996999979019165},{"id":"https://openalex.org/keywords/gradient-based-optimization","display_name":"gradient-based optimization","score":0.9559999704360962},{"id":"https://openalex.org/keywords/trust-region-optimization","display_name":"trust-region optimization","score":0.9010000228881836},{"id":"https://openalex.org/keywords/akaike-information-criterion","display_name":"Akaike information criterion","score":0.8460000157356262},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.7799999713897705},{"id":"https://openalex.org/keywords/model-calibration","display_name":"model calibration","score":0.8569999933242798},{"id":"https://openalex.org/keywords/computational-efficiency","display_name":"computational efficiency","score":0.8069999814033508},{"id":"https://openalex.org/keywords/geospatial-big-data","display_name":"geospatial big data","score":0.8349999785423279}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.6716127395629883},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5238708853721619},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.5235402584075928},{"id":"https://openalex.org/C126674687","wikidata":"https://www.wikidata.org/wiki/Q1662573","display_name":"Akaike information criterion","level":2,"score":0.5171096324920654},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.513372540473938},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47907310724258423},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.4637508988380432},{"id":"https://openalex.org/C129848803","wikidata":"https://www.wikidata.org/wiki/Q2564360","display_name":"Sample size determination","level":2,"score":0.42519518733024597},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38925355672836304},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2704996168613434},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.24689650535583496},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0982808768749237},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C58640448","wikidata":"https://www.wikidata.org/wiki/Q42515","display_name":"Cartography","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/13658816.2023.2246154","doi":"https://doi.org/10.1080/13658816.2023.2246154","is_oa":false,"landing_page_url":"https://doi.org/10.1080/13658816.2023.2246154","pdf_url":null,"source":{"id":"https://openalex.org/S4210181446","display_name":"International Journal of Geographical Information Systems","issn_l":"0269-3798","issn":["0269-3798","1362-3087"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["dongbi-b","poland-100"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Geographical Information Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W147998453","https://openalex.org/W340592063","https://openalex.org/W1971536112","https://openalex.org/W1991766386","https://openalex.org/W2029469881","https://openalex.org/W2045066934","https://openalex.org/W2047120335","https://openalex.org/W2071936897","https://openalex.org/W2085210969","https://openalex.org/W2110987058","https://openalex.org/W2747207142","https://openalex.org/W2901615696","https://openalex.org/W2912855477","https://openalex.org/W2948613401","https://openalex.org/W3005470619","https://openalex.org/W3014404004","https://openalex.org/W3019445951","https://openalex.org/W3045423387","https://openalex.org/W3046985715","https://openalex.org/W3081236293","https://openalex.org/W3095728645","https://openalex.org/W3179247283","https://openalex.org/W3186245229","https://openalex.org/W3210785432","https://openalex.org/W3216005224","https://openalex.org/W3216125977","https://openalex.org/W4301014524"],"related_works":["https://openalex.org/W3005470619","https://openalex.org/W3216005224","https://openalex.org/W4403199568","https://openalex.org/W3122392460","https://openalex.org/W4388976969","https://openalex.org/W3111564377","https://openalex.org/W7067773305","https://openalex.org/W3046985715","https://openalex.org/W7122584531","https://openalex.org/W4405481466"],"abstract_inverted_index":{"Multi-scale":[0],"geographically":[1],"weighted":[2],"regression":[3],"(MGWR)":[4],"is":[5,22,49,109],"among":[6],"the":[7,17,32,54,58,62,78,86,91,95,106,113,120,133],"most":[8],"popular":[9],"methods":[10],"to":[11,85,115,126],"analyze":[12],"non-stationary":[13],"spatial":[14,142],"relationships.":[15],"However,":[16],"current":[18,96],"model":[19,79],"calibration":[20],"algorithm":[21,131],"computationally":[23],"intensive:":[24],"its":[25,36],"runtime":[26,114],"has":[27,100],"a":[28,72,101],"cubic":[29],"growth":[30],"with":[31,45,71,124],"sample":[33,107,127],"size,":[34],"while":[35],"memory":[37,121],"use":[38,122],"grows":[39],"quadratically.":[40],"We":[41,76],"propose":[42],"calibrating":[43],"MGWR":[44,138],"gradient-based":[46],"optimization.":[47],"This":[48],"obtained":[50],"by":[51],"analytically":[52],"deriving":[53],"gradient":[55],"vector":[56],"and":[57,68,89,118,136],"Hessian":[59],"matrix":[60],"of":[61],"corrected":[63],"Akaike":[64],"information":[65],"criterion":[66],"(AICc)":[67],"wrapping":[69],"them":[70],"trust-region":[73],"optimization":[74],"algorithm.":[75],"evaluate":[77],"quality":[80],"empirically.":[81],"Our":[82,129],"method":[83,97],"converges":[84],"same":[87,92],"coefficients":[88],"produces":[90],"inference":[93],"as":[94],"but":[98],"it":[99],"substantial":[102],"computational":[103],"gain":[104],"when":[105],"size":[108],"large.":[110],"It":[111],"reduces":[112],"quadratic":[116],"convergence":[117],"makes":[119,137],"linear":[123],"respect":[125],"size.":[128],"new":[130],"outperforms":[132],"existing":[134],"alternatives":[135],"feasible":[139],"for":[140],"large":[141],"datasets.":[143]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":4}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2023-08-25T00:00:00"}
