# Burnt-Area Quick Mapping Method with Synthetic Aperture Radar Data
## 2 Materials and Methods
### Related Method  
The support vector machine (SVM) algorithm allocates pixels into classes by means of maximizing the class separation from the training data, and labels the pixels, according to the nearest class [34]. The SVM principle is to search for the best classifier which gives the largest margin of accuracy [35]. For a training set \(x=\{x_{0},x_{1},\ldots,x_{N}\}\in R^{B\times N}\), which consists of two classes that are denoted as \(L=\{-1,+1\}\), the SVM aims to maximize the hyperplane margin while minimizing the error. The optimization is solved as follows:  
\[\frac{max}{\alpha_{i}}\left\{\sum_{i=1}^{l}\alpha_{i}-\frac{1}{2}\sum_{i=1,j=1 }^{l}\alpha_{i}\alpha_{j}y_{i}y_{j}K(x,x_{i})\right\} \tag{1}\]  
where \(\alpha_{i}\) is Lagrange multipliers and K(\(x,x_{i}\)) is the kernel function, the decision function is written as follows:  
\[f(x)=\sum_{i=1}^{l}\alpha_{i}y_{i}K(x,x_{i})+b \tag{2}\]  
The SVM maps the original data into a high dimensional feature space using kernel functions and finds the optimal hyperplane that separates the true and false classes [36]. The SVM's most interesting property is its high capacity for generalization with relatively small numbers of training data points. Recent studies have suggested that the support vector machine (SVM) can provide good results for the hyperspectral remote sensing classification and superior results have been reported, compared to the traditional remote sensing classification algorithms, such as the maximum likelihood (ML), k-nearest neighbor, and neural networks (NNs) [37]. In addition to the SVM-based categorical classification, there is also growing interest in the SVM regression for estimating the subpixel land cover proportions. The SVM with the radial basis function (RBF) kernel can achieve an excellent performance in classification/prediction tasks, due to the following facts: First, the RBF kernel can map a sample to a higher dimensional space, and the linear kernel function is essentially a special case of the RBF. Meanwhile, the kernel of the RBF and the sigmoid have  
Figure 2: The advantages of the SAR data, compared to the optical sensors for the detection of the burn scar areas where visually, it is not covered by clouds and smoke. a similar performance with certain parameters. Second, compared with the polynomial kernel function, only a few parameters need to be modulated by the RBF and the number of kernel function parameters directly influences the complexity of this function. Finally, the RBF kernel has fewer numerical difficulties [36]. The random forest method generates an ensemble of regression trees through the aggregated sampling of the training data. At each decision tree's node, a random selection parameter of the predictor variables is evaluated for their ability to split the training data into respective target classes, with the variable leading to the most homogeneous classification being selected [38]. Previous studies revealed that the random forest algorithm was acceptable to map the burnt scars area, by showing an overall accuracy >0.90 [39]. The decision tree-based algorithm and support vector machine was are also powerful to identify the burnt areas with an accuracy 0.85-0.91 and >0.99, respectively [40; 41]. In line with the development of the field of artificial intelligence, image processing methods also develop by making use of artificial intelligence functions. Several artificial intelligence methods that are widely used in image processing are artificial neural networks or ANNs. The method that has recently begun to be applied in the studies of mapping flooding potential and vulnerability, is to use machine learning [22]. Neural network classification algorithms have long been used for remote sensing image classification. Many have suggested that these types of models are superior to traditional statistical classification approaches (i.e., maximum-likelihood classification), because they do not make assumptions about the nature of the data distribution, and the function is simply learned from training samples.