{"id":"https://openalex.org/W7160018780","doi":"https://doi.org/10.1007/s10109-026-00493-8","title":"Efficiency of spatially multiscale machine learning models in addressing spatial non-stationarity and enhancing predictive accuracy","display_name":"Efficiency of spatially multiscale machine learning models in addressing spatial non-stationarity and enhancing predictive accuracy","publication_year":2026,"publication_date":"2026-04-01","ids":{"openalex":"https://openalex.org/W7160018780","doi":"https://doi.org/10.1007/s10109-026-00493-8"},"language":"en","primary_location":{"id":"doi:10.1007/s10109-026-00493-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10109-026-00493-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10109-026-00493-8.pdf","source":{"id":"https://openalex.org/S144150890","display_name":"Journal of Geographical Systems","issn_l":"1435-5930","issn":["1435-5930","1435-5949"],"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 Geographical Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10109-026-00493-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5129162429","display_name":"Daniel Bic\u00e1k","orcid":null},"institutions":[{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Daniel Bic\u00e1k","raw_affiliation_strings":["Department of Applied Geoinformatics and Cartography, Charles University, Prague, Czechia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Geoinformatics and Cartography, Charles University, Prague, Czechia","institution_ids":["https://openalex.org/I21250087"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074762720","display_name":"Luk\u00e1\u0161 Brodsk\u00fd","orcid":"https://orcid.org/0000-0003-4396-0477"},"institutions":[{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"Luk\u00e1\u0161 Brodsk\u00fd","raw_affiliation_strings":["Department of Applied Geoinformatics and Cartography, Charles University, Prague, Czechia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Geoinformatics and Cartography, Charles University, Prague, Czechia","institution_ids":["https://openalex.org/I21250087"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5074762720"],"corresponding_institution_ids":["https://openalex.org/I21250087"],"apc_list":{"value":3090,"currency":"USD","value_usd":3090},"apc_paid":{"value":3090,"currency":"USD","value_usd":3090},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.54751399,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":"2","first_page":"243","last_page":"279"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11911","display_name":"Spatial and Panel Data Analysis","score":0.847000002861023,"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":0.847000002861023,"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":0.03539999946951866,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10226","display_name":"Land Use and Ecosystem Services","score":0.012299999594688416,"subfield":{"id":"https://openalex.org/subfields/2306","display_name":"Global and Planetary Change"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/boosting","display_name":"Boosting (machine learning)","score":0.6417999863624573},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.5580999851226807},{"id":"https://openalex.org/keywords/gradient-boosting","display_name":"Gradient boosting","score":0.46799999475479126},{"id":"https://openalex.org/keywords/bandwidth","display_name":"Bandwidth (computing)","score":0.448199987411499},{"id":"https://openalex.org/keywords/spatial-variability","display_name":"Spatial variability","score":0.4449000060558319},{"id":"https://openalex.org/keywords/spatial-ecology","display_name":"Spatial ecology","score":0.4404999911785126},{"id":"https://openalex.org/keywords/multivariate-interpolation","display_name":"Multivariate interpolation","score":0.43059998750686646},{"id":"https://openalex.org/keywords/spatial-correlation","display_name":"Spatial correlation","score":0.4099999964237213},{"id":"https://openalex.org/keywords/kriging","display_name":"Kriging","score":0.39430001378059387}],"concepts":[{"id":"https://openalex.org/C46686674","wikidata":"https://www.wikidata.org/wiki/Q466303","display_name":"Boosting (machine learning)","level":2,"score":0.6417999863624573},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5679000020027161},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.5580999851226807},{"id":"https://openalex.org/C70153297","wikidata":"https://www.wikidata.org/wiki/Q5591907","display_name":"Gradient boosting","level":3,"score":0.46799999475479126},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.4580000042915344},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.448199987411499},{"id":"https://openalex.org/C94747663","wikidata":"https://www.wikidata.org/wiki/Q7574086","display_name":"Spatial variability","level":2,"score":0.4449000060558319},{"id":"https://openalex.org/C158709400","wikidata":"https://www.wikidata.org/wiki/Q3578586","display_name":"Spatial ecology","level":2,"score":0.4404999911785126},{"id":"https://openalex.org/C203332170","wikidata":"https://www.wikidata.org/wiki/Q6334079","display_name":"Multivariate interpolation","level":3,"score":0.43059998750686646},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.42640000581741333},{"id":"https://openalex.org/C150060386","wikidata":"https://www.wikidata.org/wiki/Q7574054","display_name":"Spatial correlation","level":2,"score":0.4099999964237213},{"id":"https://openalex.org/C81692654","wikidata":"https://www.wikidata.org/wiki/Q225926","display_name":"Kriging","level":2,"score":0.39430001378059387},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3804999887943268},{"id":"https://openalex.org/C169258074","wikidata":"https://www.wikidata.org/wiki/Q245748","display_name":"Random forest","level":2,"score":0.37299999594688416},{"id":"https://openalex.org/C159620131","wikidata":"https://www.wikidata.org/wiki/Q1938983","display_name":"Spatial analysis","level":2,"score":0.3653999865055084},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.35100001096725464},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.3495999872684479},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3492000102996826},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.3449999988079071},{"id":"https://openalex.org/C2780598303","wikidata":"https://www.wikidata.org/wiki/Q65921492","display_name":"Flexibility (engineering)","level":2,"score":0.3409000039100647},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.3407000005245209},{"id":"https://openalex.org/C130402806","wikidata":"https://www.wikidata.org/wiki/Q5361768","display_name":"Random field","level":2,"score":0.3312000036239624},{"id":"https://openalex.org/C2910321205","wikidata":"https://www.wikidata.org/wiki/Q1938983","display_name":"Geographically Weighted Regression","level":2,"score":0.32109999656677246},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.3158000111579895},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.30219998955726624},{"id":"https://openalex.org/C194648359","wikidata":"https://www.wikidata.org/wiki/Q3318054","display_name":"Generalized additive model","level":2,"score":0.29679998755455017},{"id":"https://openalex.org/C138695830","wikidata":"https://www.wikidata.org/wiki/Q1938983","display_name":"Spatial dependence","level":2,"score":0.2937999963760376},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.29330000281333923},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2842000126838684},{"id":"https://openalex.org/C48921125","wikidata":"https://www.wikidata.org/wiki/Q10861030","display_name":"Linear regression","level":2,"score":0.26249998807907104},{"id":"https://openalex.org/C64754055","wikidata":"https://www.wikidata.org/wiki/Q7574053","display_name":"Spatial contextual awareness","level":2,"score":0.2578999996185303},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.2572999894618988},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.2515000104904175}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10109-026-00493-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10109-026-00493-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10109-026-00493-8.pdf","source":{"id":"https://openalex.org/S144150890","display_name":"Journal of Geographical Systems","issn_l":"1435-5930","issn":["1435-5930","1435-5949"],"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 Geographical Systems","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10109-026-00493-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10109-026-00493-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10109-026-00493-8.pdf","source":{"id":"https://openalex.org/S144150890","display_name":"Journal of Geographical Systems","issn_l":"1435-5930","issn":["1435-5930","1435-5949"],"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 Geographical Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320309755","display_name":"Univerzita Karlova v Praze","ror":"https://ror.org/024d6js02"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7160018780.pdf","grobid_xml":"https://content.openalex.org/works/W7160018780.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W1829241487","https://openalex.org/W1966052311","https://openalex.org/W2024697317","https://openalex.org/W2037996624","https://openalex.org/W2043821500","https://openalex.org/W2047120335","https://openalex.org/W2063143131","https://openalex.org/W2148227415","https://openalex.org/W2311124343","https://openalex.org/W2621121878","https://openalex.org/W2747207142","https://openalex.org/W2793997912","https://openalex.org/W2803367070","https://openalex.org/W2901833745","https://openalex.org/W2911640637","https://openalex.org/W2930389570","https://openalex.org/W2968079289","https://openalex.org/W3004931647","https://openalex.org/W3019445951","https://openalex.org/W3047664852","https://openalex.org/W3089838435","https://openalex.org/W3127361658","https://openalex.org/W3156803485","https://openalex.org/W4210622816","https://openalex.org/W4283788062","https://openalex.org/W4285043263","https://openalex.org/W4294325987","https://openalex.org/W4316663647","https://openalex.org/W4386967839","https://openalex.org/W4388528020","https://openalex.org/W4390414173","https://openalex.org/W4404425198","https://openalex.org/W4409203535","https://openalex.org/W4411091431","https://openalex.org/W4412719383"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"This":[1],"study":[2],"evaluates":[3],"geographically":[4,20],"weighted":[5,21],"(GW)":[6],"machine-learning":[7],"models":[8,78,129,137,174,186],"and,":[9],"for":[10,95],"the":[11,66,91,176,188],"first":[12],"time,":[13],"introduces":[14],"and":[15,40,51,65,68,86,101,109,132,154,182],"empirically":[16],"assesses":[17],"spatially":[18],"multiscale":[19],"(SM-GW)":[22],"models,":[23],"in":[24,44,168],"which":[25],"kernel":[26],"bandwidths":[27],"vary":[28,60],"by":[29,191],"location.":[30],"We":[31],"compare":[32],"Linear":[33,96],"Regression,":[34],"Random":[35,104],"Forest,":[36,105],"Support":[37,106],"Vector":[38,107],"Machines,":[39,108],"Extreme":[41,110],"Gradient":[42,111],"Boosting":[43,112],"global":[45,81,128],"form,":[46],"with":[47,90],"single-bandwidth":[48,76,172],"GW":[49,77,173],"variants":[50],"SM-GW":[52,136,158,185],"extensions,":[53],"using":[54],"135":[55],"synthetic":[56],"datasets":[57],"that":[58,75],"systematically":[59],"spatial":[61,71,84,116,166,193],"autocorrelation,":[62],"relationship":[63],"complexity,":[64],"magnitude":[67],"form":[69],"of":[70],"non-stationarity.":[72],"Results":[73],"show":[74],"consistently":[79,140],"outperform":[80],"baselines":[82],"when":[83],"dependence":[85],"non-stationarity":[87],"are":[88],"pronounced,":[89],"largest":[92],"gains":[93],"observed":[94],"Regression":[97],"under":[98],"moderate":[99],"nonlinearity":[100],"high":[102],"autocorrelation.":[103],"also":[113],"benefit":[114],"from":[115,148],"weighting,":[117],"though":[118],"their":[119],"inherent":[120],"flexibility":[121],"limits":[122],"improvement.":[123],"Adding":[124],"geographic":[125],"coordinates":[126],"to":[127,146],"proves":[130],"unreliable":[131],"often":[133],"degrades":[134],"accuracy.":[135],"do":[138],"not":[139],"exceed":[141],"single":[142],"bandwidth":[143,152,159],"formulations":[144],"due":[145],"instability":[147],"isotropic":[149],"neighborhoods,":[150],"local":[151],"variance,":[153],"interpolation":[155],"effects.":[156],"However,":[157],"surfaces":[160],"provide":[161],"valuable":[162],"diagnostic":[163],"insight":[164],"into":[165],"variation":[167,195],"interaction":[169],"scales.":[170],"Overall,":[171],"offer":[175],"most":[177],"robust":[178],"balance":[179],"between":[180],"accuracy":[181],"stability,":[183],"while":[184],"extend":[187],"methodological":[189],"toolkit":[190],"making":[192],"scale":[194],"explicit.":[196]},"counts_by_year":[],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2026-05-05T00:00:00"}