## 2 Materials and Methods
### Construction of Optimal Identifying Feature  
One-Class SVM (OCSVM) is used for anomaly detection and outlier detection. Its goal is to identify anomalous data points that differ from the normal pattern by modeling them using only normal data. It does not need abnormal data for training, has good adaptability to high-dimensional data and complex data distributions, and can control the detection sensitivity of anomalies by adjusting the model parameters. Its key lies in how to choose a suitable hyperplane so that normal data are surrounded as much as possible and abnormal data are kept away. This is achieved by optimizing an objective function, which includes minimizing the distance from the hyperplane to the nearest normal data point and maximizing the interval between the hyperplane and the normal data [41; 42]. The model mapped the data samples to a high-dimensional feature space through a kernel function for better aggregation and solved the optimal hyperplane in the feature space to realize the maximum separation of the target data from the coordinate origin [43]. Because the data set will inevitably contain abnormal points and noise points, to maintain the accuracy of the algorithm, a slack variable will usually be introduced to reduce the error brought by the abnormal points and noise points [44; 45]. Therefore, One-Class SVM had to address the following minimization issues:  
\[\min_{\epsilon,\delta_{i},\rho}\frac{1}{2}\|\epsilon\|^{2}+\frac{1}{\vartheta \mu}\sum_{i=1}^{\mu}\delta_{i}-\rho \tag{1}\]  
\[\left(\epsilon^{T}\phi_{(x_{i})}\right)>\rho-\delta_{i},\delta_{i}>0,i=1, \ldots,n \tag{2}\]  
where \(\vartheta\) is the most important parameter that sets an upper limit for the outlier score and is also the lower term for the number of samples that are support vectors in the training dataset, \(\delta_{i}\) denotes the slack variable that allows some samples to lie on the wrong side of the separation hyperplane, \(\epsilon\) denotes the normal vector of the separation hyperplane, \(\rho\) denotes the distance from the separation hyperplane to the nearest training sample, and \(\phi_{(x_{i})}\) denotes the feature mapping function that maps the input samples to the high-dimensional space. The minimization problem was solved by employing the Lagrange operator. The resulting final decision function is shown below. \[f(x)=\text{sgn}\left(\sum_{i=1}^{m}\alpha_{i}K(x,x_{i})-\rho\right) \tag{3}\]  
where \(\alpha_{i}\) is the Lagrange operator and \(K(x,x_{i})\) is the feature vector of the input sample \(x\). The method creates a hyperplane with a parameter \(\epsilon,\rho\) that maximizes the distance from the zeros in the feature space and separates the zeros from all data points. In this study, we verified the optimal parameters for the identification of litchi fruit trees by six backscattering coefficients, VV, VH, VV + VH, VV - VH, VH/VV, and (VH - VV)/(VH + VV), composed by polarization in S-1 multitemporal images [30]. Firstly, the backscattering coefficients VV and VH (in dB) were obtained by preprocessing the GRD products; then, based on the linear combination of polarization, the feature parameters VV + VH, VV - VH, VH/VV, and (VH - VV)/(VH + VV) were calculated. Based on the polarized feature parameters, the divisibility between litchi fruit trees, cropland, and other forest and vegetation was proven (Figure 2a,c), and the single-class classification model was used to determine the optimal segmentation planes between litchi fruit trees and the other two crops (Figure 2b,d). To achieve greater precision regarding the spatial distribution of litchi fruit trees, this study combined the polarization characteristics with growth stage information and proposed three extraction factors: \(Hv\), \(Tb\), and C_D. The growth stage information revealed that the backscattering coefficient experienced a valley during the ripening period of litchi, which was succeeded by a new peak post-ripening. By combining long-time-series image data, a recognition model was developed.