{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T18:13:30Z","timestamp":1780337610422,"version":"3.54.1"},"reference-count":36,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2020,10,30]],"date-time":"2020-10-30T00:00:00Z","timestamp":1604016000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key Research and Development Project","award":["2019YFB2102500\/2019YFB2102503"],"award-info":[{"award-number":["2019YFB2102500\/2019YFB2102503"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71903183"],"award-info":[{"award-number":["71903183"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41801316"],"award-info":[{"award-number":["41801316"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>Geographically weighted regression (GWR) introduces the distance weighted kernel function to examine the non-stationarity of geographical phenomena and improve the performance of global regression. However, GWR calibration becomes critical when using a serial computing mode to process large volumes of data. To address this problem, an improved approach based on the compute unified device architecture (CUDA) parallel architecture fast-parallel-GWR (FPGWR) is proposed in this paper to efficiently handle the computational demands of performing GWR over millions of data points. FPGWR is capable of decomposing the serial process into parallel atomic modules and optimizing the memory usage. To verify the computing capability of FPGWR, we designed simulation datasets and performed corresponding testing experiments. We also compared the performance of FPGWR and other GWR software packages using open datasets. The results show that the runtime of FPGWR is negatively correlated with the CUDA core number, and the calculation efficiency of FPGWR achieves a rate of thousands or even tens of thousands times faster than the traditional GWR algorithms. FPGWR provides an effective tool for exploring spatial heterogeneity for large-scale geographic data (geodata).<\/jats:p>","DOI":"10.3390\/ijgi9110653","type":"journal-article","created":{"date-parts":[[2020,10,30]],"date-time":"2020-10-30T09:29:32Z","timestamp":1604050172000},"page":"653","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["A CUDA-Based Parallel Geographically Weighted Regression for Large-Scale Geographic Data"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3362-0631","authenticated-orcid":false,"given":"Dongchao","family":"Wang","sequence":"first","affiliation":[{"name":"School of Geomatics and Marine Information, Jiangsu Ocean University, Lianyungang 222005, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yi","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Geomatics and Marine Information, Jiangsu Ocean University, Lianyungang 222005, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Agen","family":"Qiu","sequence":"additional","affiliation":[{"name":"Research Center of Government GIS, Chinese Academy of Surveying and Mapping, Beijing 100039, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaochen","family":"Kang","sequence":"additional","affiliation":[{"name":"Research Center of Government GIS, Chinese Academy of Surveying and Mapping, Beijing 100039, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiakuan","family":"Han","sequence":"additional","affiliation":[{"name":"School of Geomatics and Marine Information, Jiangsu Ocean University, Lianyungang 222005, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhengyuan","family":"Chai","sequence":"additional","affiliation":[{"name":"School of Geomatics and Marine Information, Jiangsu Ocean University, Lianyungang 222005, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,10,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1007\/s10115-018-1186-x","article-title":"Analyzing large-scale human mobility data: A survey of machine learning methods and applications","volume":"58","author":"Toch","year":"2019","journal-title":"Knowl. Inf. Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"102470","DOI":"10.1016\/j.jtrangeo.2019.102470","article-title":"Assessment of large-scale transitions in public transport networks using open timetable data: Case of Helsinki metro extension","volume":"79","author":"Kujala","year":"2019","journal-title":"J. Transp. Geogr."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41746-019-0121-1","article-title":"Best practices for analyzing large-scale health data from wearables and smartphone apps","volume":"2","author":"Hicks","year":"2019","journal-title":"NPJ Digit. Med."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3524","DOI":"10.1109\/JSTARS.2019.2925416","article-title":"Incremental learning for semantic segmentation of large-scale remote sensing data","volume":"12","author":"Tasar","year":"2019","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1188","DOI":"10.1080\/13658816.2019.1605073","article-title":"SOVAS: A scalable online visual analytic system for big climate data analysis","volume":"34","author":"Li","year":"2020","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1007\/s10708-014-9602-6","article-title":"Data-driven geography","volume":"80","author":"Miller","year":"2015","journal-title":"GeoJournal"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Xia, J., Huang, S., Zhang, S., Li, X., Lyu, J., Xiu, W., and Tu, W. (2020). DAPR-tree: A distributed spatial data indexing scheme with data access patterns to support Digital Earth initiatives. Int. J. Digit. Earth, 1\u201316.","DOI":"10.1080\/17538947.2020.1778804"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Aji, A., Wang, F., Vo, H., Lee, R., Liu, Q., Zhang, X., and Saltz, J. (2013, January 26\u201330). Hadoop-GIS: A high performance spatial data warehousing system over MapReduce. Proceedings of the VLDB Endowment International Conference on Very Large Data Bases, Trento, Italy.","DOI":"10.14778\/2536222.2536227"},{"key":"ref_9","first-page":"647","article-title":"A mapreduce-based method for parallel calculation of bus passengers origin and destination from massive transit data","volume":"20","author":"Wu","year":"2018","journal-title":"J. Geo Inf. Sci."},{"key":"ref_10","unstructured":"Wilkinson, B., and Allen, M. (1999). Parallel Programming, Prentice Hall."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1152","DOI":"10.1080\/13658816.2012.741240","article-title":"Parallel agent-based simulation of individual-level spatial interactions within a multicore computing environment","volume":"27","author":"Gong","year":"2013","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"412","DOI":"10.1080\/13658816.2014.976569","article-title":"Massively parallel spatial point pattern analysis: Ripley\u2019s K function accelerated using graphics processing units","volume":"29","author":"Tang","year":"2015","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2068","DOI":"10.1080\/13658816.2017.1324975","article-title":"A GPU-accelerated adaptive kernel density estimation approach for efficient point pattern analysis on spatial big data","volume":"31","author":"Zhang","year":"2017","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1016\/j.envsoft.2019.02.016","article-title":"Using CUDA to accelerate uncertainty propagation modelling for landslide susceptibility assessment","volume":"115","author":"Sandric","year":"2019","journal-title":"Environ. Model. Softw."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Stojanovic, N., and Stojanovic, D. (2019). Parallelizing multiple flow accumulation algorithm using cuda and openacc. ISPRS Int. J. Geo Inf., 8.","DOI":"10.3390\/ijgi8090386"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1007\/s11442-020-1726-7","article-title":"Big geodata mining: Objective, connotations and research issues","volume":"30","author":"Pei","year":"2020","journal-title":"J. Geogr. Sci."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1111\/j.1538-4632.1996.tb00936.x","article-title":"Geographically weighted regression: A method for exploring spatial nonstationarity","volume":"28","author":"Brunsdon","year":"1996","journal-title":"Geogr. Anal."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"121309","DOI":"10.1016\/j.jclepro.2020.121309","article-title":"Re-examining the drive forces of China\u2019s industrial wastewater pollution based on GWR model at provincial level","volume":"262","author":"Zhang","year":"2020","journal-title":"J. Clean. Prod."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"121089","DOI":"10.1016\/j.jclepro.2020.121089","article-title":"Spatially and Temporally Varying Relationships between Ecological Footprint and Influencing Factors in China\u2019s Provinces Using Geographically Weighted Regression (GWR)","volume":"261","author":"Wu","year":"2020","journal-title":"J. Clean. Prod."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"122377","DOI":"10.1016\/j.jhazmat.2020.122377","article-title":"Exploration of spatially varying relationships between Pb and Al in urban soils of London at the regional scale using geographically weighted regression (GWR)","volume":"393","author":"Yuan","year":"2020","journal-title":"J. Hazard. Mater."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Hong, I., and Yoo, C. (2020). Analyzing Spatial Variance of Airbnb Pricing Determinants Using Multiscale GWR Approach. Sustainability, 12.","DOI":"10.3390\/su12114710"},{"key":"ref_22","unstructured":"Wu, S., Wang, Z., Du, Z., Huang, B., Zhang, F., and Liu, R. (2020). Geographically and temporally neural network weighted regression for modeling spatiotemporal non-stationary relationships. Int. J. Geogr. Inf. Sci., 1\u201327."},{"key":"ref_23","unstructured":"Bivand, R., Yu, D., Nakaya, T., and Garcia-Lopez, M.A. (2020). Package SPGWR, R Foundation for Statistical Computing. R Software Package."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.18637\/jss.v063.i17","article-title":"GWmodel: An R Package for Exploring Spatial Heterogeneity Using Geographically Weighted Models","volume":"63","author":"Gollini","year":"2015","journal-title":"J. Stat. Softw."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Oshan, T.M., Li, Z., Kang, W., Wolf, L.J., and Fotheringham, A.S. (2019). mgwr: A Python implementation of multiscale geographically weighted regression for investigating process spatial heterogeneity and scale. ISPRS Int. J. Geo Inf., 8.","DOI":"10.3390\/ijgi8060269"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1080\/13658816.2018.1521523","article-title":"Fast Geographically Weighted Regression (FastGWR): A scalable algorithm to investigate spatial process heterogeneity in millions of observations","volume":"33","author":"Li","year":"2019","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_27","unstructured":"Tran, H.T., Nguyen, H.T., and Tran, V.T. (2016, January 6\u20138). Large-scale geographically weighted regression on Spark. Proceedings of the 2016 Eighth International Conference on Knowledge and Systems Engineering (KSE), Hanoi, Vietnam."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"878","DOI":"10.1287\/mnsc.32.7.878","article-title":"An adaptive filter for estimating spatially-varying parameters: Application to modeling police hours spent in response to calls for service","volume":"32","author":"Foster","year":"1986","journal-title":"Manag. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"716","DOI":"10.1109\/TAC.1974.1100705","article-title":"A new look at the statistical model identification","volume":"19","author":"Akaike","year":"1974","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1016\/S0198-9715(01)00009-6","article-title":"Geographically weighted summary statistics\u2014A framework for localised exploratory data analysis","volume":"26","author":"Brunsdon","year":"2002","journal-title":"Comput. Environ. Urban Syst."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1111\/j.1467-9671.2009.01181.x","article-title":"Grid-enabling geographically weighted regression: A case study of participation in higher education in England","volume":"14","author":"Harris","year":"2010","journal-title":"Trans. GIS"},{"key":"ref_32","unstructured":"NVIDIA Corporation (2020, October 06). Compute Unified Device Architecture (CUDA). Available online: https:\/\/developer.nvidia.com\/cuda-toolkit."},{"key":"ref_33","unstructured":"Fotheringham, A.S., Brunsdon, C., and Charlton, M. (2002). Geographically Weighted Regression: The Analysis of Spatially Varying Relationships, John Wiley & Sons."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1467","DOI":"10.1080\/13658816.2010.528420","article-title":"Local least absolute deviation estimation of spatially varying coefficient models: Robust geographically weighted regression approaches","volume":"25","author":"Zhang","year":"2011","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"408","DOI":"10.1109\/12.21127","article-title":"Speedup versus efficiency in parallel systems","volume":"38","author":"Eager","year":"1989","journal-title":"IEEE Trans. Comput."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Yang, L., Sun, X., and Li, Z. (2019). An efficient framework for remote sensing parallel processing: Integrating the artificial bee colony algorithm and multiagent technology. Remote Sens., 11.","DOI":"10.3390\/rs11020152"}],"container-title":["ISPRS International Journal of Geo-Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2220-9964\/9\/11\/653\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:27:01Z","timestamp":1760178421000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2220-9964\/9\/11\/653"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,30]]},"references-count":36,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2020,11]]}},"alternative-id":["ijgi9110653"],"URL":"https:\/\/doi.org\/10.3390\/ijgi9110653","relation":{},"ISSN":["2220-9964"],"issn-type":[{"value":"2220-9964","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,10,30]]}}}