3.2.2. Machine Learning Methods

Multivariate modeling based on four common algorithms in agricultural and environmental modeling, including RFR, SVM, ANN and PLSR, was used to model the RCF. In the first scenario, all reflective band-based spectral indices were used as independent variables. In the second scenario, in addition to spectral indices based on reflective bands, VV and VH band information was also used in the modeling process. Each RFR, SVM, ANN and PLSR algorithm was calibrated based on training data (96 samples for corn, 38 samples for wheat and 84 samples for soybean). Then the efficiency of each of these algorithms in estimating the RCF fraction using test data (53 samples for corn, 20 samples for wheat and 43 samples for soybean) was evaluated.

PLSR breaks down both dependent and independent variables into a number of major components. PLSR is a two-line calibration algorithm that converts a large number of correlated linear variables into several non-correlated variables based on data compression. Hence, this algorithm can solve the challenges of high correlation between variables and overfitting in the modeling process [38].

In recent years, artificial neural networks have been widely used to estimate various environmental variables based on satellite data [39,40]. In this study, a back-propagation ANN was used to model the residue. This algorithm consists of input, hidden and output layers. Sigmoid and linear functions were used for activation in hidden and output nodes, respectively. To calibrate synaptic coefficients, the Levenberg–Marquardt minimization algorithm was used [41]. The number of nodes in the hidden layers varied between 4 to 8. To optimize the structural parameters of the ANN algorithm for the network, we changed the momentum coefficient and learning rate from 0.1 to 1.0 with a step of 0.05. The number of nodes in the hidden layer varied from 3 to 7. Mean squared error was used as a measure of the performance threshold and the determination of a network with optimal structure in receipt fraction modeling. The optimal network was selected in terms of mean absolute error between validation and predictions data.

The SVR model is a widely used algorithm for solving nonlinear problems [42]. In the SVR method, n-dimensional input variables are transferred to the new feature space with higher dimensions using the core functions and, as a result, optimal separator super planes are developed [43]. In this study, different Gaussian, linear, nonlinear quadratic, cubic, etc., kernels were evaluated, and finally the Gaussian kernel was selected and used as a function in the receipt fraction estimation process. The optimal values of box constraint, kernel scale and epsilon were set to 909, 857 and 0.04, respectively.

RFR is an ensemble-learning algorithm that combines a large set of decision trees to improve the accuracy of estimating a variable [44]. RFR has several advantages in modeling environmental variables, including (1) low sensitivity to noise and over-fitting, and (2) the use of a large number of quantitative and qualitative variables in the modeling process [45,46]. To implement this algorithm, two parameters, the number of trees and the number of attributes, must be set. The number of trees varied from 30 to 300 with step size 30 and the number of trees 150 was selected as the optimal value.

The optimal model for each of these four algorithms was selected to estimate the RCF and the mean absolute error between the validation data and the predictions.
