## 4 Support Vector Machine Models  
Machine Learning (ML) is the process of learning to convert experience into expertise. A concise explanation is that a computer program learns from the experience from data recorded in a period of time; the performance of the program is evaluated in time by improving experience [39]. In other words, ML models interpret patterns through learning based on data obtained in a period through a training process to make a prediction, generating new data that will measure the behavior of a phenomenon in the future [40; 41; 42].  
According to the literature, there are two main specific techniques that ML uses to develop learning methods using information directly from data acquired [43]. There exist two main learning methods: supervised learning that uses from present to previous data to forecast events [44; 45] and unsupervised learning that analyzes the patterns from non-classified data and deduces a function to describe the behavior of the system [46]. Additionally, there are other learning methods that derive from these principal methods: semi-supervised learning and multiple instance learning [47]. In this article, the supervised learning using a support vector machine (SVM) will be discussed. The Figure 2 summarizes the two principal methods and its most used models to predict solar radiation.  
According to [8], supervised algorithms are currently the most used, and within this method are neural networks and vector support machines. These models have been widely used in recent years, with vector support machines being recently integrated to provide new solar prediction techniques. In this context, SVM belongs to a technique called supervised learning defined as a technique for identifying the behavior between an input and an output variable [48].  
The theoretical basis of SVM is to minimize the structural risk related to the empirical risk from the training process and the confidence range from Vapnik Chervonenkis dimension (VC dimension) [49]. The complexity of the problem will be reduced when the VC dimension is smaller, making the risk smaller [50].  
The architecture of an SVM is a versatile and configurable model based on a kernel machine that could be treated as a classification or regression problem according to Vapnik equations [51], while a support vector regression is only used for regression problems [11]. Therefore, an SVM is a great alternative to solve classification problems in forecasting time series [52; 53; 54; 55].  
In order to predict a non-linear variable, such as solar radiation, it is necessary to have a data set \(x_{i}\) that represents the input data sample space, \(d_{i}\) which is the target value and to know the number of data points \(n\)[14]; therefore, it is possible to resort to [PERSON]'s equations theory. The input variables to SMV models are related to the objective variable (variable to predict), visualizing the mapped data in a non-linear function \(f(x)\)[51]:  
\[f(x)=\omega\cdot\phi(x)+b \tag{1}\]  
where \(\omega\) is the normal vector, \(b\) is a constant, also called bias term [56] and  
subject to: \[=\left\{\begin{array}{l}|y_{i}-(\langle w,x_{i}\rangle+b)\geq\epsilon+ \varsigma_{i}|\\ \langle w,x_{i}\rangle+b-y_{i}\leq\epsilon+\varsigma_{i}\\ \varsigma_{i},\varsigma_{i}^{*}\geq 0\end{array}\right.\] (5)  
To solve Equation (1), it is possible to use Lagrange and optimal constraints to obtain a non-linear regression function:  
\[f(x)=\sum_{i=1}^{l}(\alpha_{i}-\alpha_{i}^{*})K(x_{i}-x)+b \tag{6}\]  
where \(\alpha_{i},\alpha_{i}^{*}\) are Lagrange multipliers. The term \(k(x_{i}-x)\) is defined as the kernel function [55]:  
\[K(x_{i}-x)=\sum_{i=1}^{D}\phi_{i}(x)+\phi_{i}(y) \tag{7}\]  
The general architecture form of a SVM is shown in Figure 3.