## Materials and Methods
### Support Vector Machine (SVM)  
The Support vector machine, which is introduced by Vapnik, is one of the newest algorithms [30]. Different from the conventional models, SVM follows the rule of statistical machine learning process and structural risk minimization to obtain the minimal upper bound generalization error, which is the biggest advantage of SVM compared with other models. Due to this, SVM has a great popularity and a wide use in the area of pattern recognition, classification, and regression analysis and forecasting [31,32].  
**Definition 4**.: _Suppose a set of data \(\{x_{i}d_{i}\}_{i}^{n}\), the \(n\)-dimensional input vector is represented as \(x_{i}\), and the output is expressed as \(d_{i}\). The estimating function of SVM can be represented as:_  
\[f(x)=w\cdot\phi(x)+b \tag{4}\]  
_where \(\phi(x)\) is a nonlinear mapping while \(w\), \(b\) is the weight vector and scalar, separately, and they are estimated through the equation:_  
\[R_{SVMs}(C)=\frac{1}{2}\|w^{2}\|+C\frac{1}{n_{i}}\sum_{i=1}^{n}L(x_{i},d_{i}) \tag{5}\]  
Figure 1: The flowchart of the Cuckoo Search Algorithm.  
_where \(C\) represents the penalty factor of the error. The \(L(x_{i},d_{i})\) is the loss function \(C\frac{n}{2}\sum\limits_{i=1}^{n}L(x_{i},d_{i})\) represents the empirical error._  
**Definition 5.**_Setting the upper and lower excess deviation \(\xi_{i}\) and \(\xi_{i}^{*}\) as the positive slack variables, the optimization problem is obtained as the follows:_  
\[MinimizeR_{SVMs}(w,\xi^{(*)})=\frac{1}{2}\|w^{2}\|+C\frac{1}{n}\sum\limits_{i= 1}^{n}\left(\xi_{i}+\xi_{i}^{*}\right) \tag{6}\]  
\[\text{Subject to }\left\{\begin{array}{l}d_{i}-w\phi(x_{i})-b_{i}\leq \varepsilon+\xi_{i}\\ w\phi(x_{i})+b_{i}-d_{i}\leq\varepsilon+\xi_{i}^{*}\\ \xi_{i},\xi_{i}^{*}\geq 0,i=1,\ldots,l\end{array}\right. \tag{7}\]  
_where \(w^{2}/2\) represents the regularization term. \(\varepsilon\) stands for the loss factor, and its value is related to the approximate accuracy of the input sample. \(l\) represents the quantity of elements in the sample data series._  
Equation (4) can be explained through the Lagrange function, which is described as follows:  
\[f(x)=\sum\limits_{i=1}^{n}\left(\alpha_{i}-\alpha_{i}^{*}\right)K(x,x_{i})+b \tag{8}\]  
where \(\alpha_{i}\) and \(\alpha_{i}^{*}\) are the multipliers of Lagrange function. \(K(x,x_{i})\) represents the kernel function and \(K(x_{i},x_{j})=\phi(x_{i})\phi(x_{j})\), which is the dot product of the two inner vectors \(x_{i}\), \(x_{j}\) in \(\phi(x_{i})\) and \(\phi(x_{j})\).  
Gaussian function, which is known for its features of simplicity, efficiency, and reliable computing ability, has proved to be one of the most effective core functions [30]. SVM model, which employs it as the core function, can effectively obtain the complex features of nonlinearity of the original data and result sample by matching input data into a higher-dimensional feature space.  
**Definition 6.**_Gaussian function, which is employed as core function of SVM model, is described as follows:_  
\[K(\mathbf{x}_{i},\mathbf{x}_{j})=\exp\Bigl{(}-\gamma\|\mathbf{x}_{i}-\mathbf{x}_{j}\|^{2} \Bigr{)} \tag{9}\]  
_where the \(\gamma\) stands for the parameter of the kernel function. \(\mathbf{x}_{i}\), \(\mathbf{x}_{j}\) are vector quantities in the input space._  
In this paper, parameters (\(\gamma\), C), which are considered as the two most valuable figures that influence the performance of wind speed prediction. The CSO is used to optimize them.