{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T16:13:54Z","timestamp":1772554434299,"version":"3.50.1"},"reference-count":29,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,12,13]],"date-time":"2022-12-13T00:00:00Z","timestamp":1670889600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["42050103"],"award-info":[{"award-number":["42050103"]}],"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":["2021C01031"],"award-info":[{"award-number":["2021C01031"]}],"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":["2022C25021"],"award-info":[{"award-number":["2022C25021"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Provincial Key Research and De-velopment Program of Zhejiang","award":["42050103"],"award-info":[{"award-number":["42050103"]}]},{"name":"Provincial Key Research and De-velopment Program of Zhejiang","award":["2021C01031"],"award-info":[{"award-number":["2021C01031"]}]},{"name":"Provincial Key Research and De-velopment Program of Zhejiang","award":["2022C25021"],"award-info":[{"award-number":["2022C25021"]}]},{"name":"Key project of Soft Science Research of Zhejiang Province in the year 2022","award":["42050103"],"award-info":[{"award-number":["42050103"]}]},{"name":"Key project of Soft Science Research of Zhejiang Province in the year 2022","award":["2021C01031"],"award-info":[{"award-number":["2021C01031"]}]},{"name":"Key project of Soft Science Research of Zhejiang Province in the year 2022","award":["2022C25021"],"award-info":[{"award-number":["2022C25021"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>Geographically neural network weighted regression is an improved model of GWR combined with a neural network. It has a stronger ability to fit nonlinear functions, and complex geographical processes can be modeled more fully. GNNWR uses the distance metric of Euclidean space to express the relationship between sample points. However, except for spatial location features, geographic entities also have many diverse attribute features. Incorporating attribute features into the modeling process can make the model more suitable for the real geographical process. Therefore, we proposed a spatial-attribute proximities deep neural network to aggregate data from the spatial feature and attribute feature, so that one unified distance metric can be used to express the spatial and attribute relationships between sample points at the same time. Based on GNNWR, we designed a spatial and attribute neural network weighted regression (SANNWR) model to adapt to this new unified distance metric. We developed one case study to examine the effectiveness of SANNWR. We used PM2.5 concentration data in China as the research object and compared the prediction accuracy between GWR, GNNWR and SANNWR. The results showed that the \u201cspatial-attribute\u201d unified distance metric is useful, and that the SANNWR model showed the best performance.<\/jats:p>","DOI":"10.3390\/ijgi11120620","type":"journal-article","created":{"date-parts":[[2022,12,14]],"date-time":"2022-12-14T02:54:21Z","timestamp":1670986461000},"page":"620","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Spatial and Attribute Neural Network Weighted Regression for the Accurate Estimation of Spatial Non-Stationarity"],"prefix":"10.3390","volume":"11","author":[{"given":"Sihan","family":"Ni","sequence":"first","affiliation":[{"name":"Faculty of Information Science and Engineering, Ocean University of China, 238 Songling Road, Qingdao 266100, China"}]},{"given":"Zhongyi","family":"Wang","sequence":"additional","affiliation":[{"name":"Huawei Technologies, Zhangheng Road, Shenzhen 518129, China"}]},{"given":"Yuanyuan","family":"Wang","sequence":"additional","affiliation":[{"name":"Ocean Academy, Zhejiang University, 1 Zheda Road, Zhoushan 316021, China"},{"name":"Zhejiang Provincial Key Laboratory of Geographic Information Science, 148 Tianmushan Road, Hangzhou 310028, China"}]},{"given":"Minghao","family":"Wang","sequence":"additional","affiliation":[{"name":"Huawei Technologies, Zhangheng Road, Shenzhen 518129, China"}]},{"given":"Shuqi","family":"Li","sequence":"additional","affiliation":[{"name":"Huawei Technologies, Zhangheng Road, Shenzhen 518129, China"}]},{"given":"Nan","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Science and Technology, Ningbo University, No. 521 Wenwei Rd. Baisha Road St. Cixi, Ningbo 315300, China"},{"name":"Ningbo Bay Area Development Research Base, No. 521 Wenwei Rd. Baisha Road St. Cixi, Ningbo 315300, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1111\/j.1365-3121.1992.tb00605.x","article-title":"Statistics for spatial data","volume":"4","author":"Cressie","year":"1992","journal-title":"Terra Nova"},{"key":"ref_2","unstructured":"Cressie, N., and Wikle, C.K. (2015). Statistics for Spatio-Temporal Data, John Wiley & Sons."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1111\/gean.12071","article-title":"Geographical and temporal weighted regression (GTWR)","volume":"47","author":"Fotheringham","year":"2015","journal-title":"Geogr. 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