Spatial neural network

Openshaw (1993) and Hewitson et al. (1994) started investigating the applications of the a-spatial/classic NNs to geographic phenomena.{{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}}{{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}} 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 relations between the geo-spatial datasets' variables. 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.{{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 }} Thereafter scientists developed several categories of SNNs – see below.

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 dependence/autocorrelation, spatial heterogeneity, spatial association/cross-correlation) from the geo-locations of the geo-spatial datasets’ (statistical) individuals/units.{{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}}{{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 }}

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 weights and designing a spatial structure from the originally a-spatial/classic neural networks.
• 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. They generally outperform the OSFA spatial neural networks, but they do not consistently handle the spatial heterogeneity at multiple scales.{{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 }}
• 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.{{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 }} Like the SVANNs, they do not consistently handle spatial heterogeneity at multiple scales.

There exist case-study applications of SNNs in:

• energy for predicting the electricity consumption;{{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 }}
• agriculture for classifying the vegetation;{{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 }}
• real estate for appraising the premises.{{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}}

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• Statistics
• Neural networks' supercategories
• Statistical software
• Quantitative geography
• Spatial analysis
• GIS software

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Category:Neural network architectures

Category:Spatial analysis