# Assessing the Added Value of Sentinel-1 PolSAR Data for Crop Classification
## 3 Methods
### Genetic Algorithm
This might be explained by the fact that the full feature space contains plenty of redundant features and, consequently, implementing GA with very large chromosomes does not lead to better outcomes. Based on Figure 5b, the relationship between chromosome length and the mean generation time appears to be proportional. This experimental result is quite reasonable, considering that the greater the number of genes (features) contained in a chromosome, the more computational time is needed for training the SVM classifier for each one of population's chromosomes. Aiming to extract an optimal subset of spectral-temporal features with rich information content for accurately discriminating the crop types of the studied agricultural region, we considered the value of 80 genes as an optimal one for the implementation of GA, close to the minimum threshold (70 genes), in order to achieve the highest possible classification accuracy with the lowest possible computational cost. A second-degree polynomial SVM was employed as the function for assessing the ability of each chromosome to effectively discriminate the crop types of the study area at each iteration. SVM is a non-parametric supervised machine learning algorithm [127]. This model depends on three important hyperparameters, namely the cost parameter \(\mathcal{C}\), kernel bandwidth \(\gamma\), and the independent term of the kernel function, denoted by _coef_. The cost parameter determines the acceptable number of misclassification errors and sig  
Figure 5: (**a**) The maximum weighted f1 score obtained for different values of chromosome length. (**b**) The mean generation time required for different values of chromosome length. nificantly affects model's generalization ability [128]. In other words, the higher the cost parameter value, the higher the penalties imposed for margin violations [129], resulting in the formation of complex decision boundaries and overfitting [107; 130]. The complexity of the decision boundary also depends on the \(\gamma\) parameter, which determines the influence range of its training sample [131]. The kernel's independent term _coeff_ determines the degree of influence of the high-degree polynomials versus low-degree polynomials in the classification model [131]. In our implementation, SVM was parameterized as follows: cost parameter = 1, independent coefficient = 1, and gamma parameter = 0.01. This parametrization was based on preliminary experiments in order to combine high performance with low computational complexity. Weighted-averaged f1 score, a classification accuracy metric, was used as the fitness value of the chromosomes, which is calculated based on the support of each class [132]. Next, a probabilistic selection strategy was employed, i.e., the roulette wheel or fitness proportional selection method [86], for choosing the fittest parent chromosomes to take part in the crossover process. In more detail, according to this method, the probability \(p(i)\) of a chromosome \(i\) to be selected is proportionate to its fitness value \(f(i)\) and is calculated using the formula \(p(i)=\frac{f(i)}{\sum_{i=1}^{n}f(i)}\) (n is the population size). Apart from selecting parent chromosomes with the roulette wheel method, an elitism strategy was applied, conveying the Darwinian principle of \"survival of the fittest\" [91]. By adopting this strategy, the fittest chromosomes of each generation are retained and included in the set of parent chromosomes. More specifically the percentage of the elite parents was set to 20% of the total number of parent chromosomes. After the selection process, single point crossover was employed [120]. According to this method, each pair of successive parent chromosomes participates in a probabilistic crossover process with a probability of 0.9. If crossover occurs, a particular point is randomly selected, where parent chromosomes are split into two parts, and exchange their genetic material for creating a pair of two new chromosomes.