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{{Short description|Category of tailored neural networks}}
{{distinguish|Spatial network}}{{other uses|SNN (disambiguation)}}
<onlyinclude>'''Spatial neural networks''' ('''SNNs''') or '''geographically weighted neural networks''' ('''GWNNs'''), 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]], 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 |doi=10.1103/PhysRevE.101.042301}}</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}}</ref><ref name="Hagenauer et al. (2021)">{{cite journal |vauthors=Hagenauer J, Helbich M |date=2022 |title=A geographically weighted artificial neural network |journal=International journal of geographical information science |volume=36 |issue=2 |pages=215–235 |doi=10.1080/13658816.2021.1871618}}</ref><includeonly>Examples of SNNs are OSFA spatial neural networks, SVANNs and GWNNs.</includeonly></onlyinclude>
==History==
Openshaw (1993) and Hewitson et al. (1994) started investigating the applications of the a-spatial/classic NNs to geographic phenomena.<ref name="Openshaw (1993)">{{cite book |vauthors=Openshaw S |date=1993 |chapter=Modelling spatial interaction using a neural net |title=Geographic information systems, spatial modelling and policy evaluation |veditors=Fischer M, Nijkamp P |publisher=Springer |___location=Berlin |isbn=978-3-642-77500-0 |doi=10.1007/978-3-642-77500-0_10}}</ref><ref name="Hewitson et al. (1994)">{{cite book |vauthors= Hewitson B, Crane R |date=1994 |title=Neural nets: applications in geography |pages=196 |publisher=Springer |___location=Berlin |isbn=978-94-011-1122-5 |doi=10.1007/978-94-011-1122-5}}</ref> They observed that a-spatial/classic NNs outperform the other extensively applied a-spatial/classic statistical models (e.g. regression models, clustering algorithms, maximum likelihood classifications) in [[geography]], especially when there exist non-linear [[Relation (mathematics)|relations]] between the geo-spatial datasets' [[Variable and attribute (research)|variables]].<ref name="Openshaw (1993)"/><ref name="Hewitson et al. (1994)"/> Thereafter, Openshaw (1998) also compared these a-spatial/classic NNs with other modern and original a-spatial statistical models at that time (i.e. fuzzy logic models, genetic algorithm models); he concluded that the a-spatial/classic NNs are statistically competitive.<ref name="Openshaw (1998)">{{cite journal |vauthors=Openshaw S |date=1998 |title=Neural network, genetic, and fuzzy logic models of spatial interaction |journal=Environment and planning |volume=30 |issue=10 |doi=10.1068/a301857}}</ref> Thereafter scientists developed several categories of SNNs – see below.
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==Categories==
There exist several categories of methods/approaches for designing and applying SNNs.
*'''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)"
*'''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. (2021)"
==See also==
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