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Spatial neural network

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This is an old revision of this page, as edited by 7e8y (talk | contribs) at 09:54, 15 March 2023 (improve: i.consistency – i.e. correct a semantic mistake hindering the understanding that NNs and SNNs generally outperform the other a-spatial/classic and spatial statistical models in presence of non-linear relations between variables; ii.meaningfulness – i.e. consistently use the term 'a-spatial/classic' through the entire entry/article for avoiding confusions). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

Spatial neural networks (SNNs) or geographically weighted neural networks (GWNNs), constitute a supercategory of tailored neural networks (NNs) for representing and predicting geographic phenomena. They generally improve both the statistical accuracy and reliability of the a-spatial/classic NNs whenever they handle geo-spatial datasets, and also of the other spatial (statistical) models (e.g. spatial regression models) whenever the geo-spatial datasets' variables depict non-linear relations.[1][2][3]

History

Openshaw (1993) and Hewitson et al. (1994) started investigating the applications of the a-spatial/classic NNs to geographic phenomena.[4][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.[4][5] 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.[6] 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, SNNs/GWNNs, 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.[7][8][3][9]

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 weights and designing a spatial structure from the originally a-spatial/classic neural networks.[1].
  • 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[2] They generally outperform the OSFA spatial neural networks, but they do not consistently handle the spatial heterogeneity at multiple scales.[10]
  • 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[3][9]. Like the SVANNs they do not consistently handle the spatial heterogeneity at multiple scales.[3]

See also

References

  1. ^ a b Morer I, Cardillo A, Díaz-Guilera A, Prignano L, Lozano S (2020). "Comparing spatial networks: a one-size-fits-all efficiency-driven approach". Physical review. 101 (4). doi:10.1103/PhysRevE.101.042301.
  2. ^ a b Gupta J, Molnar C, Xie Y, Knight J, Shekhar S (2021). "Spatial variability aware deep neural networks (SVANN): a general approach". ACM Transactions on intelligent systems and technology. 12 (6): 1–21. doi:10.1145/3466688.
  3. ^ a b c d Hagenauer J, Helbich M (2022). "A geographically weighted artificial neural network". International journal of geographical information science. 36 (2): 215–235. doi:10.1080/13658816.2021.1871618.
  4. ^ a b Openshaw S (1993). "Modelling spatial interaction using a neural net". In Fischer M, Nijkamp P (eds.). Geographic information systems, spatial modelling and policy evaluation. Berlin: Springer. doi:10.1007/978-3-642-77500-0_10. ISBN 978-3-642-77500-0.
  5. ^ a b Hewitson B, Crane R (1994). Neural nets: applications in geography. Berlin: Springer. p. 196. doi:10.1007/978-94-011-1122-5. ISBN 978-94-011-1122-5.
  6. ^ Openshaw S (1998). "Neural network, genetic, and fuzzy logic models of spatial interaction". Environment and planning. 30 (10). doi:10.1068/a301857.
  7. ^ Anselin L (2017). A local indicator of multivariate spatial association: extending Geary’s C (PDF) (Report). Center for Spatial Data Science. p. 27.
  8. ^ Fotheringham S, Sachdeva M (2021). "Modelling spatial processes in quantitative human geography". Annals of GIS. doi:10.1080/19475683.2021.1903996.
  9. ^ a b Lu B, Hu Y, Yang D, Liu Y, Liao L, Yin Z, Xia T, Dong Z, Harris P, Brunsdon C, Comber A, Dong G (2023). "GWmodelS: A software for geographically weighted models". SoftwareX. 21. doi:10.1016/j.softx.2022.101291.
  10. ^ Xie Y, Chen W, He E, Jia X, Bao H, Zhou X, Ghosh E, Ravirathinam P (2023). "Harnessing heterogeneity in space with statistically guided meta-learning". Knowledge and information systems. doi:10.1007/s10115-023-01847-0.
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