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{{distinguish|Spatial network}}
{{other uses|SNN (disambiguation)}}
[[File:GWNN and GWR prediction differences.jpg |thumb |upright=1.50
<!-- 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><noinclude>'''Spatial neural networks''' ('''SNNs''')
==History==
[[Stan Openshaw|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 |pages=147–164 |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 |series=The GeoJournal Library |volume=29 |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 |pages=1857–1872 |doi=10.1068/a301857|bibcode=1998EnPlA..30.1857O |s2cid=14290821 }}</ref> Thereafter scientists developed several categories of SNNs – see below.
==Spatial models==
Spatial statistical models (aka geographically weighted models, or merely spatial models) like the geographically weighted regressions (GWRs), 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 |doi-access=free }}</ref><ref name="Hagenauer et al. (2022)"/><ref name="Lu et al. (2023)"/>
==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)"/> 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 |volume=65 |issue=6 |pages=2699–2729 |doi=10.1007/s10115-023-01847-0|pmid=37035130 |s2cid=257436979 |pmc=9994417 |bibcode=2023KIS....65.2699X }}</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. (2022)"/><ref name="Lu et al. (2023)">{{cite journal |vauthors=Lu B, Hu Y, Yang D, Liu Y, Liao L, Yin Z, Xia T, Dong Z, Harris P, Brunsdon C, Comber A, Dong G |date=2023 |title=GWmodelS: A software for geographically weighted models |journal=SoftwareX |volume=21 |page=101291 |doi=10.1016/j.softx.2022.101291|bibcode=2023SoftX..2101291L |url=https://eprints.whiterose.ac.uk/194864/7/1-s2.0-S2352711022002096-main.pdf }}</ref> Like the SVANNs, they do not consistently handle spatial heterogeneity at multiple scales.<ref name="Hagenauer et al. (2022)"/>
==Applications==
<!-- thematic section within a methodological entry should remain a list, so that readers can quickly find examples of applications in their thematic fields/subfields; illustrative syntheses of case studies should appear within a separate/new Wikipedia’s entry (e.g. on 'applications of spatial models'); a section: 'software' reviewing the 'application software' and 'libraries/packages' with snippets of source codes would be really informative -->
There exist [[case-study]] applications of SNNs in:
* [[energy industry|energy]] for predicting the [[Electric energy consumption|electricity consumption]];<ref name="Rif'an et al. (2019)">{{cite journal |vauthors= Rif'an M, Daryanto D, Agung A |date=2019 |title=Spatial neural network for forecasting energy consumption of Palembang area |journal=Journal of Physics: Conference Series |volume=1402 |issue=3 |page=033092 |doi=10.1088/1742-6596/1402/3/033092|s2cid=237302678 |doi-access=free |bibcode=2019JPhCS1402c3092R }}</ref>
* [[agriculture]] for classifying the [[vegetation]];<ref name="Podlipnov et al. (2023)">{{cite conference |vauthors=Podlipnov V, Firsov N, Ivliev N, Mashkov S, Ishkin P, Skidanov R, Nikonorov A |date=2023 |title=Spectral-spatial neural network classification of hyperspectral vegetation images |book-title= IOP conference series: earth and environmental science |volume=1138 |doi=10.1088/1755-1315/1138/1/012040|doi-access=free }}</ref>
* [[real estate]] for appraising the [[premises]].<ref name="Lin et al. (2021)">{{cite journal |vauthors=Lin R, Ou C, Tseng K, Bowen D, Yung K, Ip W |date=2021 |title=The Spatial neural network model with disruptive technology for property appraisal in real estate industry |journal=Technological Forecasting and Social Change |volume=177 |page=121067 |doi=10.1016/j.techfore.2021.121067}}</ref><ref name="Hagenauer et al. (2022)" />
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{{reflist}}
[[Category:Neural network architectures]]
[[Category:Spatial analysis]]
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