In this study,we present a collection of local models,termed geographically weighted(GW)models,which can be found within the GWmodel R package.A GW model suits situations when spatial data are poorly described by the ...In this study,we present a collection of local models,termed geographically weighted(GW)models,which can be found within the GWmodel R package.A GW model suits situations when spatial data are poorly described by the global form,and for some regions the localized fit provides a better description.The approach uses a moving window weighting technique,where a collection of local models are estimated at target locations.Commonly,model parameters or outputs are mapped so that the nature of spatial heterogeneity can be explored and assessed.In particular,we present case studies using:(i)GW summary statistics and a GW principal components analysis;(ii)advanced GW regression fits and diagnostics;(iii)associated Monte Carlo significance tests for non-stationarity;(iv)a GW discriminant analysis;and(v)enhanced kernel bandwidth selection procedures.General Election data-sets from the Republic of Ireland and US are used for demonstration.This study is designed to complement a companion GWmodel study,which focuses on basic and robust GW models.展开更多
As an established spatial analytical tool,Geographically Weighted Regression(GWR)has been applied across a variety of disciplines.However,its usage can be challenging for large datasets,which are increasingly prevalen...As an established spatial analytical tool,Geographically Weighted Regression(GWR)has been applied across a variety of disciplines.However,its usage can be challenging for large datasets,which are increasingly prevalent in today’s digital world.In this study,we propose two high-performance R solutions for GWR via Multi-core Parallel(MP)and Compute Unified Device Architecture(CUDA)techniques,respectively GWR-MP and GWR-CUDA.We compared GWR-MP and GWR-CUDA with three existing solutions available in Geographically Weighted Models(GWmodel),Multi-scale GWR(MGWR)and Fast GWR(FastGWR).Results showed that all five solutions perform differently across varying sample sizes,with no single solution a clear winner in terms of computational efficiency.Specifically,solutions given in GWmodel and MGWR provided acceptable computational costs for GWR studies with a relatively small sample size.For a large sample size,GWR-MP and FastGWR provided coherent solutions on a Personal Computer(PC)with a common multi-core configuration,GWR-MP provided more efficient computing capacity for each core or thread than FastGWR.For cases when the sample size was very large,and for these cases only,GWR-CUDA provided the most efficient solution,but should note its I/O cost with small samples.In summary,GWR-MP and GWR-CUDA provided complementary high-performance R solutions to existing ones,where for certain data-rich GWR studies,they should be preferred.展开更多
基金presented in this paper was funded by a Strategic Research Cluster grant(07/SRC/I1168)by Science Foundation Ireland under the National Development Plan.
文摘In this study,we present a collection of local models,termed geographically weighted(GW)models,which can be found within the GWmodel R package.A GW model suits situations when spatial data are poorly described by the global form,and for some regions the localized fit provides a better description.The approach uses a moving window weighting technique,where a collection of local models are estimated at target locations.Commonly,model parameters or outputs are mapped so that the nature of spatial heterogeneity can be explored and assessed.In particular,we present case studies using:(i)GW summary statistics and a GW principal components analysis;(ii)advanced GW regression fits and diagnostics;(iii)associated Monte Carlo significance tests for non-stationarity;(iv)a GW discriminant analysis;and(v)enhanced kernel bandwidth selection procedures.General Election data-sets from the Republic of Ireland and US are used for demonstration.This study is designed to complement a companion GWmodel study,which focuses on basic and robust GW models.
基金supported by National Key Research and Development Program of China[grant num-ber 2021YFB3900904]the National Natural Science Foundation of China[grant numbers 42071368,U2033216,41871287].
文摘As an established spatial analytical tool,Geographically Weighted Regression(GWR)has been applied across a variety of disciplines.However,its usage can be challenging for large datasets,which are increasingly prevalent in today’s digital world.In this study,we propose two high-performance R solutions for GWR via Multi-core Parallel(MP)and Compute Unified Device Architecture(CUDA)techniques,respectively GWR-MP and GWR-CUDA.We compared GWR-MP and GWR-CUDA with three existing solutions available in Geographically Weighted Models(GWmodel),Multi-scale GWR(MGWR)and Fast GWR(FastGWR).Results showed that all five solutions perform differently across varying sample sizes,with no single solution a clear winner in terms of computational efficiency.Specifically,solutions given in GWmodel and MGWR provided acceptable computational costs for GWR studies with a relatively small sample size.For a large sample size,GWR-MP and FastGWR provided coherent solutions on a Personal Computer(PC)with a common multi-core configuration,GWR-MP provided more efficient computing capacity for each core or thread than FastGWR.For cases when the sample size was very large,and for these cases only,GWR-CUDA provided the most efficient solution,but should note its I/O cost with small samples.In summary,GWR-MP and GWR-CUDA provided complementary high-performance R solutions to existing ones,where for certain data-rich GWR studies,they should be preferred.
