## 3 Materials and Methods
### Accuracy Assessment and Smallholder Maize Area Estimation  
The models and experiments were evaluated using standard statistical analysis, i.e., confusion matrix, cross-validation, overall accuracy, precision, recall, F1-Score, and McNemar's test [50; 51]. These statistical measures have been used to evaluate different machine learning algorithms, such examples include, but are not limited to, [PERSON] et al. [52], [PERSON] et al. [53], and [PERSON] et al. [54]. The confusion matrix is constructed by comparing the results from the classification algorithm with the reference data collected in the field [55]. The matrix can be used to derive accuracy statistics for the map. Such statistical values include overall accuracy, kappa coefficient of agreement (\(\hat{k}\)), and conditional kappa coefficient of agreement (\(\hat{k}_{i}\)). These values are computed using Equations (1), (2), and (3 according to [PERSON] and [PERSON] [56]):  
\[\text{Overall accuracy}=\frac{\sum\limits_{i=1}^{k}x_{ii}}{N}, \tag{1}\]  
\[\hat{k}=\frac{N\sum\limits_{i=1}^{k}x_{ii}-\sum\limits_{i=1}^{k}\left(x_{i+} \times x_{+j}\right)}{N^{2}-\sum\limits_{i=1}^{k}\left(x_{i+}\times x_{+j} \right)}, \tag{2}\]  
\[\hat{k}_{i}=\frac{N(x_{ii})-\left(x_{i+}\times x_{+j}\right)}{N(x_{i+})-\left( x_{i+}\times x_{+j}\right)}, \tag{3}\]  
where k is the land cover classes in the confusion matrix, \(x_{i+}\) and \(x_{+j}\) represent marginal total for row \(i\) and column \(j\). \(x_{ii}\) represents the number of observations in row \(i\) and column \(i\). \(N\) represents total number of samples. The overall accuracy describes the proportion of the area mapped correctly. It provides a user with a probability that a randomly selected location on a map is correctly classified [57]. Kappa values that are more than 80% indicate good agreement between the reference and derived classification map. The \(\hat{k}\) measures the overall level of agreement between the reference data and the model data. The \(\hat{k}_{i}\) allows computation of the level of agreement between the reference data and the model data for a specific class \(i\). Precision measures the ability of the algorithm not to label a true positive sample (\(tp\)) or a sample that is false positive (\(fp\)). Recall measures the ability of the algorithm to find all the true positives, and false negative is represented by \(fn\). F1-Score is the harmonic mean  
Figure 4: The variance explained by the VV, VH, and VV/VH components. The first three components, which explained greater than 70% of the variance, were selected. calculated from both precision and recall values. These statistical values are calculated according to Equation (4) [55; 58; 59]:  
\[ \begin{array}{l}\text{precision }=\frac{tp}{tp+fp},\\ \text{recall }=\frac{tp}{tp+fn},\\ \text{F1}-\text{Score }=(1+\beta^{2})\frac{precision\times recall}{\beta^{2} \times precision+recall},\text{where }\beta=1.\end{array}  \tag{4}\]  
Cross-validation is another statistical method used to evaluate the performance of the model by dividing the data into k-folds (e.g., a standard value of 10 folds was used); the algorithm uses one set of data as training and the other sets are used to evaluate the model. During this iterative process, the accuracy score is calculated. The final cross-validation value is derived of the average accuracies from each iterative process. The superiority and significance between the SVM and Xgboost algorithms for each experiment were evaluated using a non-parametric [PERSON]'s statistical test [60; 61; 62]. The test is based on chi-square (\(\chi^{2}\)) statistics, calculated using Equation (5):  
\[\chi^{2}=\frac{\left(\left|f_{12}-f_{21}\right|-1\right)^{2}}{\left(f_{12}+f_{ 21}\right)}, \tag{5}\]  
where \(f_{12}\) denotes the number of cases that are wrongly classified by Model 1 but correctly classified by Model 2, and \(f_{21}\) denotes the number of cases that are correctly classified by Model 1 but wrongly classified by Model 2 [63].