Spatial neural network explained

Spatial neural network should not be confused with Spatial network.

Spatial neural networks (SNNs)Spatial neural networks (SNNs) 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]} Examples of SNNs are the OSFA spatial neural networks, SVANNs and GWNNs.

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 (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.^{[7] [8] [3]}

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.^[9]
• 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] [10]} Like the SVANNs, they do not consistently handle spatial heterogeneity at multiple scales.^[3]

Applications

There exist case-study applications of SNNs in:

• energy for predicting the electricity consumption;^[11]
• agriculture for classifying the vegetation;^[12]
• real estate for appraising the premises.^[13]

See also

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

Notes and References

1. 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 . 042301 . 10.1103/PhysRevE.101.042301. 32422764 . 2020PhRvE.101d2301M . 2445/161417 . 49564277 . free .
2. 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 . 10.1145/3466688. 244786699 .
3. Hagenauer J, Helbich M . 2022 . A geographically weighted artificial neural network . International Journal of Geographical Information Science . 36 . 2 . 215 - 235 . 10.1080/13658816.2021.1871618. 233883395 . free . 2022IJGIS..36..215H .
4. Book: Openshaw S . 1993 . Modelling spatial interaction using a neural net . Geographic information systems, spatial modelling and policy evaluation . 147–164 . Fischer M, Nijkamp P . Springer . Berlin . 978-3-642-77500-0 . 10.1007/978-3-642-77500-0_10.
5. Book: Hewitson B, Crane R . 1994 . Neural nets: applications in geography . The GeoJournal Library . 29 . 196 . Springer . Berlin . 978-94-011-1122-5 . 10.1007/978-94-011-1122-5.
6. Openshaw S . 1998 . Neural network, genetic, and fuzzy logic models of spatial interaction . Environment and Planning . 30 . 10 . 1857–1872 . 10.1068/a301857. 1998EnPlA..30.1857O . 14290821 .
7. Anselin L . 2017 . A local indicator of multivariate spatial association: extending Geary's C . Center for Spatial Data Science . 27 .
8. Fotheringham S, Sachdeva M . 2021 . Modelling spatial processes in quantitative human geography . Annals of GIS . 28 . 5–14 . 10.1080/19475683.2021.1903996. 233574813 . free .
9. 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 . 65 . 6 . 2699–2729 . 10.1007/s10115-023-01847-0. 37035130 . 257436979 . 9994417 .
10. 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 . 101291 . 10.1016/j.softx.2022.101291. 2023SoftX..2101291L .
11. Rif'an M, Daryanto D, Agung A . 2019 . Spatial neural network for forecasting energy consumption of Palembang area . Journal of Physics: Conference Series . 1402 . 3 . 033092 . 10.1088/1742-6596/1402/3/033092. 237302678 . free . 2019JPhCS1402c3092R .
12. Podlipnov V, Firsov N, Ivliev N, Mashkov S, Ishkin P, Skidanov R, Nikonorov A . 2023 . Spectral-spatial neural network classification of hyperspectral vegetation images . IOP conference series: earth and environmental science . 1138 . 10.1088/1755-1315/1138/1/012040. free .
13. Lin R, Ou C, Tseng K, Bowen D, Yung K, Ip W . 2021 . The Spatial neural network model with disruptive technology for property appraisal in real estate industry . Technological Forecasting and Social Change . 177 . 121067 . 10.1016/j.techfore.2021.121067.