## 2 Materials and Methods
### Methods
#### 2.3.3 Machine Learning Models

Table 3: The synthetic minority oversampling technique. The random forest classifier employs the Gini index as an attribute selection metric, quantifying an attribute's impurity about the classes. For a given training set T, the Gini index can be expressed as:  
\[\sum\sum_{j\
eq i}(f(C_{i},T)/\left|T\right|)\left(f(C_{i},T)/\left|T\right|\right) \tag{2}\]  
where \(f\left(C_{i},T\right)/\left|T\right|\) is the probability that the selected instance belongs to class \(C_{i}\). Each time, a tree is built to its maximum depth utilizing a mix of features on new training data. These mature trees are unpruned, which is a significant benefit of the random forest classifier over other decision tree techniques. The findings indicate that the pruning strategies used, rather than the attribute selection criteria, affect the performance of tree-based classifiers [34]. 3. Support Vector Machine  
The support vector machine (SVM) is a machine learning algorithm, first introduced by [PERSON] et al. [35]. SVM is a supervised classification method that reshapes the nonlinear environment into the linear and makes it a processable and straightforward class through the generation of hyperplane. The kernel function is the mathematical function that is utilized for data transformation. SVM translates the original input into a high-dimensional feature space using the training dataset. A separating hyperplane is produced between the points of various tree classes in the original space of n coordinates. SVM calculates the maximum separation between classes and creates a classification hyperplane in the center of the maximum margin. If the point is above the hyperplane, it is categorized as +1; otherwise, it is classified as \(-1\). Then, the properties of new data can be used to forecast which group a new record should belong to. Support vectors are the training points closest to the hyperplane. Following the acquisition of the decision surface, new data can be classified. After obtaining the decision surface, it can be used to categorize additional data. The technique is specified over a vector space. The decision surface for linearly separable space is a hyperplane, which can be represented as (Equation (3)):  
\[wx+b=0 \tag{3}\]  
The vector \(w\) and constant \(b\) are learnt using a training set of linearly separable items, where \(x\) is an arbitrary object to be categorized. SVM was suggested to handle a linearly restricted quadratic programming problem such as Equation (4), with the result that the SVM solution is always globally optimum. \[\text{min}_{\omega}\frac{1}{2}\parallel\omega\parallel^{2}+C\sum_{i}\xi_{i} \tag{4}\]  
with constraints  
\[y_{i}(x_{i}w+b)\geqslant 1-\xi_{i}\,\xi_{i}\geqslant 0,\forall i \tag{5}\]  
The original input data is transformed into a higher dimensional space using a non-linear mapping for linearly inseparable objects, and the linearly separating hyperplane can also be found in the new space without increasing the quadratic programming problem's computation complexity by using the kernel function [36]. To put it another way, to compute the similarities between the vectors in higher dimensions space for the linearly inseparable issue, the kernel function is utilized to deduce these similarities in the original lower dimensional space.