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improve: completeness – i.e. add an image of an application of a SNN vs. a spatial regression from Hagenauer et al. 2022, which depicts the differences between their predictions |
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{{Short description|Category of tailored neural networks}}
{{distinguish|Spatial network}}
{{other uses|SNN (disambiguation)}} [[File:GWNN and GWR prediction differences.jpg |thumb |upright=1.50 |top |Difference in predicted house prices in the states of Austria, from a GWR and a GWNN whose the weighting metrics use Euclidean distance (ED) and travel time distance (TTD). <ref name="Hagenauer et al. (2022)" />]]
<!-- please be cautious in revising the lead/introduction since its visible and invisible texts transclude in the entry/article on: 'spatial analysis' and 'types of artificial neural networks'; please read the webpages: 'Wikipedia:INCLUDEONLY' and 'Wikipedia:PARTRANS', for understanding the properties and purposes of the used HTML tags --><onlyinclude>'''Spatial neural networks''' ('''SNNs''') constitute a supercategory of tailored [[artificial neural networks|neural networks (NNs)]] for representing and predicting geographic phenomena. They generally improve both the statistical [[Accuracy and precision|accuracy]] and [[Statistical reliability|reliability]] of the a-spatial/classic NNs whenever they handle [[Geographic data and information| geo-spatial datasets]]<!-- if you transform 'geo-spatial' into 'geospatial' or conversely, please apply the transformation everywhere -->, and also of the other spatial [[Statistical model|(statistical) models]] (e.g. spatial regression models) whenever the geo-spatial [[data set|datasets]]' variables depict [[Nonlinear system|non-linear relations]].<ref name="Morer et al. (2020)">{{cite journal |vauthors=Morer I, Cardillo A, Díaz-Guilera A, Prignano L, Lozano S |date=2020 |title=Comparing spatial networks: a one-size-fits-all efficiency-driven approach |journal=Physical Review |volume=101 |issue=4 |page=042301 |doi=10.1103/PhysRevE.101.042301|pmid=32422764 |hdl=2445/161417 |s2cid=49564277 }}</ref><ref name="Gupta et al. (2021)">{{cite journal |vauthors=Gupta J, Molnar C, Xie Y, Knight J, Shekhar S |date=2021 |title=Spatial variability aware deep neural networks (SVANN): a general approach |journal=ACM Transactions on Intelligent Systems and Technology |volume=12 |issue=6 |pages=1–21 |doi=10.1145/3466688|s2cid=244786699 }}</ref><ref name="Hagenauer et al. (
==History==
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==Spatial models==
Spatial statistical models (aka geographically weighted models, or merely spatial models) like the geographically weighted regressions, SNNs, etc., are spatially tailored (a-spatial/classic) statistical models, so to learn and model the deterministic components of the [[spatial variability]] (i.e. [[Spatial analysis#Spatial dependence|spatial dependence/autocorrelation]], [[spatial heterogeneity]], [[Spatial analysis#Spatial association|spatial association/cross-correlation]]) from the geo-locations of the geo-spatial datasets’ [[Statistical unit|(statistical) individuals/units]].<ref name="Anselin (2017)">{{cite report |author=Anselin L |date=2017 |title=A local indicator of multivariate spatial association: extending Geary's C |publisher=Center for Spatial Data Science |pages=27 |url=https://geodacenter.github.io/docs/LA_multivariateGeary1.pdf}}</ref><ref name="Fotheringham et al. (2021)">{{cite journal |vauthors=Fotheringham S, Sachdeva M |date=2021 |title=Modelling spatial processes in quantitative human geography |journal=Annals of GIS |volume=28 |pages=5–14 |doi=10.1080/19475683.2021.1903996|s2cid=233574813 }}</ref><ref name="Hagenauer et al. (
==Categories==
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*'''One-Size-Fits-all (OSFA) spatial neural networks''', use the OSFA method/approach for globally computing the spatial [[Weighting|weights]] and designing a spatial [[structure]] from the originally a-spatial/classic neural networks.<ref name="Morer et al. (2020)"/>
*'''Spatial Variability Aware Neural Networks''' ('''SVANNs''') use an enhanced OSFA method/approach that locally recomputes the spatial weights and redesigns the spatial structure of the originally a-spatial/classic NNs, at each geo-___location of the (statistical) individuals/units' attributes' values.<ref name="Gupta et al. (2021)"/> They generally outperform the OSFA spatial neural networks, but they do not consistently handle the spatial heterogeneity at multiple scales.<ref name="Xie et al. (2023)">{{cite journal |vauthors=Xie Y, Chen W, He E, Jia X, Bao H, Zhou X, Ghosh E, Ravirathinam P |date=2023 |title=Harnessing heterogeneity in space with statistically guided meta-learning |journal=Knowledge and Information Systems |doi=10.1007/s10115-023-01847-0|s2cid=257436979 }}</ref>
*'''Geographically Weighted Neural Networks''' ('''GWNNs''') are similar to the SVANNs but they use the so-called Geographically Weighted Model (GWM) method/approach by Lu et al. (2023), so to locally recompute the spatial weights and redesign the spatial structure of the originally a-spatial/classic neural networks.<ref name="Hagenauer et al. (
==Applications==
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