TY  - JOUR
AU  - Sekulić, Aleksandar
AU  - Kilibarda, Milan
AU  - Heuvelink, Gerard B. M.
AU  - Nikolić, Mladen
AU  - Bajat, Branislav
PY  - 2020
UR  - https://www.mdpi.com/2072-4292/12/10/1687
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1973
AB  - For many decades, kriging and deterministic interpolation techniques, such as inverse distance weighting and nearest neighbour interpolation, have been the most popular spatial interpolation techniques. Kriging with external drift and regression kriging have become basic techniques that benefit both from spatial autocorrelation and covariate information. More recently, machine learning techniques, such as random forest and gradient boosting, have become increasingly popular and are now often used for spatial interpolation. Some attempts have been made to explicitly take the spatial component into account in machine learning, but so far, none of these approaches have taken the natural route of incorporating the nearest observations and their distances to the prediction location as covariates. In this research, we explored the value of including observations at the nearest locations and their distances from the prediction location by introducing Random Forest Spatial Interpolation (RFSI). We compared RFSI with deterministic interpolation methods, ordinary kriging, regression kriging, Random Forest and Random Forest for spatial prediction (RFsp) in three case studies. The first case study made use of synthetic data, i.e., simulations from normally distributed stationary random fields with a known semivariogram, for which ordinary kriging is known to be optimal. The second and third case studies evaluated the performance of the various interpolation methods using daily precipitation data for the 2016–2018 period in Catalonia, Spain, and mean daily temperature for the year 2008 in Croatia. Results of the synthetic case study showed that RFSI outperformed most simple deterministic interpolation techniques and had similar performance as inverse distance weighting and RFsp. As expected, kriging was the most accurate technique in the synthetic case study. In the precipitation and temperature case studies, RFSI mostly outperformed regression kriging, inverse distance weighting, random forest, and RFsp. Moreover, RFSI was substantially faster than RFsp, particularly when the training dataset was large and high-resolution prediction maps were made.
PB  - MDPI
T2  - Remote Sensing
T1  - Random Forest Spatial Interpolation
IS  - 10
SP  - 1687
VL  - 12
DO  - 10.3390/rs12101687
ER  - 

@article{
author = "Sekulić, Aleksandar and Kilibarda, Milan and Heuvelink, Gerard B. M. and Nikolić, Mladen and Bajat, Branislav",
year = "2020",
abstract = "For many decades, kriging and deterministic interpolation techniques, such as inverse distance weighting and nearest neighbour interpolation, have been the most popular spatial interpolation techniques. Kriging with external drift and regression kriging have become basic techniques that benefit both from spatial autocorrelation and covariate information. More recently, machine learning techniques, such as random forest and gradient boosting, have become increasingly popular and are now often used for spatial interpolation. Some attempts have been made to explicitly take the spatial component into account in machine learning, but so far, none of these approaches have taken the natural route of incorporating the nearest observations and their distances to the prediction location as covariates. In this research, we explored the value of including observations at the nearest locations and their distances from the prediction location by introducing Random Forest Spatial Interpolation (RFSI). We compared RFSI with deterministic interpolation methods, ordinary kriging, regression kriging, Random Forest and Random Forest for spatial prediction (RFsp) in three case studies. The first case study made use of synthetic data, i.e., simulations from normally distributed stationary random fields with a known semivariogram, for which ordinary kriging is known to be optimal. The second and third case studies evaluated the performance of the various interpolation methods using daily precipitation data for the 2016–2018 period in Catalonia, Spain, and mean daily temperature for the year 2008 in Croatia. Results of the synthetic case study showed that RFSI outperformed most simple deterministic interpolation techniques and had similar performance as inverse distance weighting and RFsp. As expected, kriging was the most accurate technique in the synthetic case study. In the precipitation and temperature case studies, RFSI mostly outperformed regression kriging, inverse distance weighting, random forest, and RFsp. Moreover, RFSI was substantially faster than RFsp, particularly when the training dataset was large and high-resolution prediction maps were made.",
publisher = "MDPI",
journal = "Remote Sensing",
title = "Random Forest Spatial Interpolation",
number = "10",
pages = "1687",
volume = "12",
doi = "10.3390/rs12101687"
}

Sekulić, A., Kilibarda, M., Heuvelink, G. B. M., Nikolić, M.,& Bajat, B.. (2020). Random Forest Spatial Interpolation. in Remote Sensing
MDPI., 12(10), 1687.
https://doi.org/10.3390/rs12101687

Sekulić A, Kilibarda M, Heuvelink GBM, Nikolić M, Bajat B. Random Forest Spatial Interpolation. in Remote Sensing. 2020;12(10):1687.
doi:10.3390/rs12101687 .

Sekulić, Aleksandar, Kilibarda, Milan, Heuvelink, Gerard B. M., Nikolić, Mladen, Bajat, Branislav, "Random Forest Spatial Interpolation" in Remote Sensing, 12, no. 10 (2020):1687,
https://doi.org/10.3390/rs12101687 . .

TY  - JOUR
AU  - Pejović, Milutin
AU  - Nikolić, Mladen
AU  - Heuvelink, Gerard B. M.
AU  - Hengl, Tomislav
AU  - Kilibarda, Milan
AU  - Bajat, Branislav
PY  - 2018
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/943
AB  - An approach for using lasso (Least Absolute Shrinkage and Selection Operator) regression in creating sparse 3D models of soil properties for spatial prediction at multiple depths is presented. Modeling soil properties in 3D benefits from interactions of spatial predictors with soil depth and its polynomial expansion, which yields a large number of model variables (and corresponding model parameters). Lasso is able to perform variable selection, hence reducing the number of model parameters and making the model more easily interpretable. This also prevents overfitting, which makes the model more accurate. The presented approach was tested using four variable selection approaches - none, stepwise, lasso and hierarchical lasso, on four kinds of models - standard linear model, linear model with polynomial expansion of depth, linear model with interactions of covariates with depth and linear model with interactions of covariates with depth and its polynomial expansion. This framework was used to predict Soil Organic Carbon (SOC) in three contrasting study areas: Bor (Serbia), Edgeroi (Australia) and the Netherlands. Results show that lasso yields substantial improvements in accuracy over standard and stepwise regression - up to 50 % of total variance. It yields models which contain up to five times less nonzero parameters than the full models and that are usually more sparse than models obtained by stepwise regression, up to three times. Extension of the standard linear model by including interactions typically improves the accuracy of models produced by lasso, but is detrimental to standard and stepwise regression. Regarding computation time, it was demonstrated that lasso is several orders of magnitude more efficient than stepwise regression for models with tens or hundreds of variables (including interactions). Proper model evaluation is emphasized. Considering the fact that lasso requires meta-parameter tuning, standard cross-validation does not suffice for adequate model evaluation, hence a nested cross-validation was employed. The presented approach is implemented as publicly available sparsereg3D R package.
PB  - Elsevier Ltd
T2  - Computers & Geosciences
T1  - Sparse regression interaction models for spatial prediction of soil properties in 3D
EP  - 13
SP  - 1
VL  - 118
DO  - 10.1016/j.cageo.2018.05.008
ER  - 

@article{
author = "Pejović, Milutin and Nikolić, Mladen and Heuvelink, Gerard B. M. and Hengl, Tomislav and Kilibarda, Milan and Bajat, Branislav",
year = "2018",
abstract = "An approach for using lasso (Least Absolute Shrinkage and Selection Operator) regression in creating sparse 3D models of soil properties for spatial prediction at multiple depths is presented. Modeling soil properties in 3D benefits from interactions of spatial predictors with soil depth and its polynomial expansion, which yields a large number of model variables (and corresponding model parameters). Lasso is able to perform variable selection, hence reducing the number of model parameters and making the model more easily interpretable. This also prevents overfitting, which makes the model more accurate. The presented approach was tested using four variable selection approaches - none, stepwise, lasso and hierarchical lasso, on four kinds of models - standard linear model, linear model with polynomial expansion of depth, linear model with interactions of covariates with depth and linear model with interactions of covariates with depth and its polynomial expansion. This framework was used to predict Soil Organic Carbon (SOC) in three contrasting study areas: Bor (Serbia), Edgeroi (Australia) and the Netherlands. Results show that lasso yields substantial improvements in accuracy over standard and stepwise regression - up to 50 % of total variance. It yields models which contain up to five times less nonzero parameters than the full models and that are usually more sparse than models obtained by stepwise regression, up to three times. Extension of the standard linear model by including interactions typically improves the accuracy of models produced by lasso, but is detrimental to standard and stepwise regression. Regarding computation time, it was demonstrated that lasso is several orders of magnitude more efficient than stepwise regression for models with tens or hundreds of variables (including interactions). Proper model evaluation is emphasized. Considering the fact that lasso requires meta-parameter tuning, standard cross-validation does not suffice for adequate model evaluation, hence a nested cross-validation was employed. The presented approach is implemented as publicly available sparsereg3D R package.",
publisher = "Elsevier Ltd",
journal = "Computers & Geosciences",
title = "Sparse regression interaction models for spatial prediction of soil properties in 3D",
pages = "13-1",
volume = "118",
doi = "10.1016/j.cageo.2018.05.008"
}

Pejović, M., Nikolić, M., Heuvelink, G. B. M., Hengl, T., Kilibarda, M.,& Bajat, B.. (2018). Sparse regression interaction models for spatial prediction of soil properties in 3D. in Computers & Geosciences
Elsevier Ltd., 118, 1-13.
https://doi.org/10.1016/j.cageo.2018.05.008

Pejović M, Nikolić M, Heuvelink GBM, Hengl T, Kilibarda M, Bajat B. Sparse regression interaction models for spatial prediction of soil properties in 3D. in Computers & Geosciences. 2018;118:1-13.
doi:10.1016/j.cageo.2018.05.008 .

Pejović, Milutin, Nikolić, Mladen, Heuvelink, Gerard B. M., Hengl, Tomislav, Kilibarda, Milan, Bajat, Branislav, "Sparse regression interaction models for spatial prediction of soil properties in 3D" in Computers & Geosciences, 118 (2018):1-13,
https://doi.org/10.1016/j.cageo.2018.05.008 . .