gesjGEOGRAPHY, ENVIRONMENT, SUSTAINABILITYGEOGRAPHY, ENVIRONMENT, SUSTAINABILITY2071-93882542-1565Russian Geographical Society10.24057/2071-9388-2025-3240gesj-3985Research ArticleRESEARCH PAPERСтатьиIndividual And Pairwise Representativeness Of Sampling Points In Interpolation Tasks Of Heavy Metals Distribution In The TopsoilBaglaevaElena M.

S. Kovalevskaya str., 20, Ekaterinburg, 620990

elenbaglaeva@gmail.comSergeevAleksandr P.

S. Kovalevskaya str., 20, Ekaterinburg, 620990

ShichkinAndrey V.

S. Kovalevskaya str., 20, Ekaterinburg, 620990

BuevichAlexander G.

S. Kovalevskaya str., 20, Ekaterinburg, 620990

Institute of Industrial Ecology UB RASRussian Federation202507042025181613Copyright © Baglaeva E.M., Sergeev A.P., Shichkin A.V., Buevich A.G., 20252025Baglaeva E.M., Sergeev A.P., Shichkin A.V., Buevich A.G.Baglaeva E.M., Sergeev A.P., Shichkin A.V., Buevich A.G.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://ges.rgo.ru/jour/article/view/3985

The optimization of environmental soil monitoring based on representative selection of a training subset for an artificial neural network is an unresolved problem in the tasks of interpolation of the distribution of metals in the topsoil. The soil survey data, often used as input for artificial neural network modeling, are datasets at irregular points. Usually, the division of the input data into training and test subsets is carried out randomly in a ratio of 70% to 30% points, respectively. The question of the individual and collective representativeness of local sampling points on the element content in the soil in a given area for a training subset remains beyond the scope of interpolation problems. In this work, the representativeness of the sampling points plays a crucial role in reducing the ANN error and enhancing the correlation between the results of model calculations on the test subset and natural measurements when the points are part of the training subset. When evaluating the pairwise representativeness, we found two types of effects: synergy and anti-synergy. The synergy was achieved with an increase in model accuracy when the pair entered the training subset. The anti-synergy manifested in a decrease informativeness of the point pair for modeling. The various sampling locations have different information and unequal meaning for feature interpolation. The scale-free network structures were found to have pairwise representativeness by RMSE.

representativenesssamplingheavy metalsartificial neural networkstraining subsetReferencesBaglaeva E.M., Sergeev A.P., Shichkin A.V., Buevich A. G. (2020). The Effect of Splitting of Raw Data into Training and Test Subsets on the Accuracy of Predicting Spatial Distribution by a Multilayer Perceptron. Math. Geosci., 52, 111–121.Baglaeva E.M., Sergeev A.P., Shichkin A.V., Buevich A. G. (2020). The Effect of Splitting of Raw Data into Training and Test Subsets on the Accuracy of Predicting Spatial Distribution by a Multilayer Perceptron. Math. Geosci., 52, 111–121.Baglaeva E.M., Sergeev A.P., Shichkin A.V., Buevich A.G. (2021). The Extraction of the training subset for the spatial distribution modelling of the heavy metal in topsoil. Catena, 207, 105699. https://doi.org/10.1016/j.catena.2021.105699Baglaeva E.M., Sergeev A.P., Shichkin A.V., Buevich A.G. (2021). The Extraction of the training subset for the spatial distribution modelling of the heavy metal in topsoil. Catena, 207, 105699. https://doi.org/10.1016/j.catena.2021.105699Boussange V., Pellissier L. (2022). Eco-evolutionary model on spatial graphs reveals how habitat structure affects phenotypic differentiation. Communications Biology, 5, 668. https://doi.org/10.1038/s42003-022-03595-3Boussange V., Pellissier L. (2022). Eco-evolutionary model on spatial graphs reveals how habitat structure affects phenotypic differentiation. Communications Biology, 5, 668. https://doi.org/10.1038/s42003-022-03595-3Dale M.R. and Fortin M. (2010). From graphs to spatial graphs. Annu. Rev. Ecol. Evol. Syst., 41, 21–38.Dale M.R. and Fortin M. (2010). From graphs to spatial graphs. Annu. Rev. Ecol. Evol. Syst., 41, 21–38.Demyanov V., Gloaguen E., Kanevski M. (2020). A special issue on data science for geosciences. Math. Geosci., 52, 1–3.Demyanov V., Gloaguen E., Kanevski M. (2020). A special issue on data science for geosciences. Math. Geosci., 52, 1–3.Fernandez Jaramillo J.M. and Mayerle R. (2018). Sample selection via angular distance in the space of the arguments of an artificial neural network. Computers and Geosciences, 114, 98–106.Fernandez Jaramillo J.M. and Mayerle R. (2018). Sample selection via angular distance in the space of the arguments of an artificial neural network. Computers and Geosciences, 114, 98–106.Gutierrez-Velez V.H. and Wiese D. (2020). Sampling bias mitigation for species occurrence modeling using machine learning methods. Ecological Informatics, 58, 101091. https://doi.org/10.1016/j.ecoinf.2020.101091.Gutierrez-Velez V.H. and Wiese D. (2020). Sampling bias mitigation for species occurrence modeling using machine learning methods. Ecological Informatics, 58, 101091. https://doi.org/10.1016/j.ecoinf.2020.101091.Kramm T. and Hoffmeister D. (2020). Assessing the influence of environmental factors and datasets on soil type prediction with two machine learning algorithms in a heterogeneous area in the Rur catchment, Germany. Geoderma Regional, 22, e00316. https://doi.org/10.1016/j.geodrs.2020.e00316.Kramm T. and Hoffmeister D. (2020). Assessing the influence of environmental factors and datasets on soil type prediction with two machine learning algorithms in a heterogeneous area in the Rur catchment, Germany. Geoderma Regional, 22, e00316. https://doi.org/10.1016/j.geodrs.2020.e00316.Legendre P., Dale M.R.T., Fortin M.J., et. al. (2004). Effects of spatial structures on the results of field experiments. Ecology, 85(12), 3202–3214.Legendre P., Dale M.R.T., Fortin M.J., et. al. (2004). Effects of spatial structures on the results of field experiments. Ecology, 85(12), 3202–3214.Levin S.A. (2002). Complex adaptive systems: Exploring the known, the unknown and the unknowable. Bull. Am. Math. Soc., 40, 3–20.Levin S.A. (2002). Complex adaptive systems: Exploring the known, the unknown and the unknowable. Bull. Am. Math. Soc., 40, 3–20.Liu Q., Li H., Guo L., et. al. (2022). Digital mapping of soil organic carbon density using newly developed bare soil spectral indices and deep neural network. Catena, 219, 106603. https://doi.org/10.1016/j.catena.2022.106603.Liu Q., Li H., Guo L., et. al. (2022). Digital mapping of soil organic carbon density using newly developed bare soil spectral indices and deep neural network. Catena, 219, 106603. https://doi.org/10.1016/j.catena.2022.106603.Malof J.M., Reichman D., Collins L.M. (2018). How do we choose the best model? The impact of cross-validation design on model evaluation for buried threat detection in ground penetrating radar. Proceedings. 10628, Detection and Sensing of Mines, Explosive Objects, and Obscured Targets XXIII, 106280C. https://doi.org/10.1117/12.2305793Malof J.M., Reichman D., Collins L.M. (2018). How do we choose the best model? The impact of cross-validation design on model evaluation for buried threat detection in ground penetrating radar. Proceedings. 10628, Detection and Sensing of Mines, Explosive Objects, and Obscured Targets XXIII, 106280C. https://doi.org/10.1117/12.2305793de Mello D.C., Ferreira T.O., Veloso G.V., et. al. (2022). Pedogenetic processes operating at different intensities inferred by geophysical sensors and machine learning algorithms. Catena, 216, Part A, 106370, ISSN 0341-8162. https://doi.org/10.1016/j.catena.2022.106370.de Mello D.C., Ferreira T.O., Veloso G.V., et. al. (2022). Pedogenetic processes operating at different intensities inferred by geophysical sensors and machine learning algorithms. Catena, 216, Part A, 106370, ISSN 0341-8162. https://doi.org/10.1016/j.catena.2022.106370.Nath A. and Subbiah K. (2018). The role of pertinently diversified and balanced training as well as testing data sets in achieving the true performance of classifiers in predicting the antifreeze proteins. Neurocomputing, 272, 294–305.Nath A. and Subbiah K. (2018). The role of pertinently diversified and balanced training as well as testing data sets in achieving the true performance of classifiers in predicting the antifreeze proteins. Neurocomputing, 272, 294–305.O’Brien D., Manseau M., Fall A., Fortin M-J. (2006). Testing the importance of spatial configuration of winter habitat for woodland caribou: An application of graph theory. Biological Conservation, 130, 70–83.O’Brien D., Manseau M., Fall A., Fortin M-J. (2006). Testing the importance of spatial configuration of winter habitat for woodland caribou: An application of graph theory. Biological Conservation, 130, 70–83.O’Hare M.T., Gunn I.D.M., Critchlow-Watton N., et. al. (2020). Fewer sites but better data? Optimising the representativeness and statistical power of a national monitoring network. Ecological Indicators, 114, 106321. https://doi.org/10.1016/j.ecolind.2020.106321.O’Hare M.T., Gunn I.D.M., Critchlow-Watton N., et. al. (2020). Fewer sites but better data? Optimising the representativeness and statistical power of a national monitoring network. Ecological Indicators, 114, 106321. https://doi.org/10.1016/j.ecolind.2020.106321.Pesch R., Schröder W., Dieffenbach-Fries H., et. al. (2008). Improving the design of environmental monitoring networks. Case study on the heavy metals in mosses survey in Germany. Ecological Informatics, 3(1), 111 121. https://doi.org/10.1016/j.ecoinf.2007.11.001.Pesch R., Schröder W., Dieffenbach-Fries H., et. al. (2008). Improving the design of environmental monitoring networks. Case study on the heavy metals in mosses survey in Germany. Ecological Informatics, 3(1), 111 121. https://doi.org/10.1016/j.ecoinf.2007.11.001.Prager S.D. and Reiners W.A. (2009). Historical and emerging practices in ecological topology. Ecological complexity, 6, 160–171. doi:10.1016/j.ecocom.2008.11.001Prager S.D. and Reiners W.A. (2009). Historical and emerging practices in ecological topology. Ecological complexity, 6, 160–171. doi:10.1016/j.ecocom.2008.11.001Shichkin A.V., Buevich A.G., Sergeev A.P., et. al. (2018). Prediction of the content of anomalously distributed chromium in the soil by hybrid models based on artificial neural networks. Geoecology. Engineering geology. Hydrogeology. Geocryology, 3, 86 96. [in Russian] Urban D.L., Minor E.S., Treml E.A., Schick R.S. (2009). Graph models of habitat mosaics. Ecology Letters, 12, 260–73.Shichkin A.V., Buevich A.G., Sergeev A.P., et. al. (2018). Prediction of the content of anomalously distributed chromium in the soil by hybrid models based on artificial neural networks. Geoecology. Engineering geology. Hydrogeology. Geocryology, 3, 86 96. [in Russian] Urban D.L., Minor E.S., Treml E.A., Schick R.S. (2009). Graph models of habitat mosaics. Ecology Letters, 12, 260–73.Wang I.J. and Bradburd G.S. (2014). Isolation by environment. Molecular Ecology, https://doi.org/10.1111/mec.12938Wang I.J. and Bradburd G.S. (2014). Isolation by environment. Molecular Ecology, https://doi.org/10.1111/mec.12938Wang X., An Sh., Xu Y., et. al. (2020). A back propagation neural network model optimized by mind evolutionary algorithm for estimating Cd, Cr, and Pb concentrations in soils using Vis-NIR diffuse reflectance spectroscopy. Applied Sciences, 10(51), 1 17. https://doi:10.3390/app10010051Wang X., An Sh., Xu Y., et. al. (2020). A back propagation neural network model optimized by mind evolutionary algorithm for estimating Cd, Cr, and Pb concentrations in soils using Vis-NIR diffuse reflectance spectroscopy. Applied Sciences, 10(51), 1 17. https://doi:10.3390/app10010051Wang Y., Ma H., Wang J., et. al. (2021). Hyperspectral monitor of soil chromium contaminant based on deep learning network model in the Eastern Junggar coalfield. Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy, 257, 119739. https://doi.org/10.1016/j.saa.2021.119739.Wang Y., Ma H., Wang J., et. al. (2021). Hyperspectral monitor of soil chromium contaminant based on deep learning network model in the Eastern Junggar coalfield. Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy, 257, 119739. https://doi.org/10.1016/j.saa.2021.119739.Xu Q., Zhu A-X., Liu J. (2023). Land-use change modeling with cellular automata using land natural evolution unit. Catena, 224, 106998. https://doi.org/10.1016/j.catena.2023.106998.Xu Q., Zhu A-X., Liu J. (2023). Land-use change modeling with cellular automata using land natural evolution unit. Catena, 224, 106998. https://doi.org/10.1016/j.catena.2023.106998.Zhu A.X., Liu J., Du F., et.al. (2015). Predictive soil mapping with limited sample data. European Journal of Soil Science. 66, 535–547. doi: 10.1111/ejss.12244Zhu A.X., Liu J., Du F., et.al. (2015). Predictive soil mapping with limited sample data. European Journal of Soil Science. 66, 535–547. doi: 10.1111/ejss.12244Zhu A.X., Lu G., Liu J., et. al. (2018). Spatial prediction based on Third Law of Geography. Annals of GIS, 24 (4), 225–240. https://doi.org/10.1080/19475683.2018.1534890Zhu A.X., Lu G., Liu J., et. al. (2018). Spatial prediction based on Third Law of Geography. Annals of GIS, 24 (4), 225–240. https://doi.org/10.1080/19475683.2018.1534890Zhu A.X., Lv G.N., Zhou C.H., et al. (2020). Geographic similarity: Third Law of Geography? Journal of Geoinformation Science, 22(4), 673–679. https://doi.org/10.12082/dqxxkx.2020.200069.Zhu A.X., Lv G.N., Zhou C.H., et al. (2020). Geographic similarity: Third Law of Geography? Journal of Geoinformation Science, 22(4), 673–679. https://doi.org/10.12082/dqxxkx.2020.200069.Zhong L., Guo X., Xu Zh., Ding M. (2021). Soil properties: Their prediction and feature extraction from the LUCAS spectral library using deep convolutional neural networks. Geoderma, 402, 115366.Zhong L., Guo X., Xu Zh., Ding M. (2021). Soil properties: Their prediction and feature extraction from the LUCAS spectral library using deep convolutional neural networks. Geoderma, 402, 115366.Ziggah Y.Y., Youjian H., Tierra A.R., Laari P.B. (2019). Coordinate Transformation between Global and Local Data Based on Artificial Neural Network with K-Fold Cross-Validation in Ghana. Earth Sciences Research Journal, 23(1), 67 77. https://doi.org/10.15446/esrj.v23n1.63860.Ziggah Y.Y., Youjian H., Tierra A.R., Laari P.B. (2019). Coordinate Transformation between Global and Local Data Based on Artificial Neural Network with K-Fold Cross-Validation in Ghana. Earth Sciences Research Journal, 23(1), 67 77. https://doi.org/10.15446/esrj.v23n1.63860.

The authors declare that there are no conflicts of interest present.