## 3 Methodology: Proposed SybilSocNet Algorithm
### ML Terminologies and Methodologies Applied in This Study
#### 3.1.3 Support Vector Machine Algorithm (SVM)  
SVM, a supervised learning algorithm, operates on labeled datasets, aiming to learn a hyperplane that separates data points into distinct classes [58]. Its training optimizes the hyperplane's position for effective classification of new points [59]. When assessing a new point's position relative to the hyperplane, SVM assigns it to an appropriate class. In Figure 5, the hyperplane visually separates red dots from green stars, with dashed lines indicating the distance between the hyperplane and the nearest support vectors [27; 60]. Such support vector positioning during training determines the hyperplane's position and margin size [40]. In this testing phase, the hyperplane functions as the class boundary [61], classifying new instances. SVM's hyperplane is crucial for classification and regression tasks, predicting class or value for new instances, relying upon the new instance's position with respect to the hyperplane [62; 63]. Based on the hyperplane distance, the instance receives a specific class or value based on the problem type. For instance, in a classification problem, the trained SVM algorithm predicts the class of a new instance. After training and hyperplane positioning, the algorithm assigns an instance to a class. If the brown rhombus falls to the hyperplane's left side, associated with green stars, the algorithm predicts it as a duck (assuming green  
Figure 5: The hyperplane for SVM. Colors and shapes represent different items categories. stars are ducks and red dots are lions). Similarly, the purple triangle and pink hexagon on the hyperplane's right side belong to the lion class. Consequently, the algorithm predicts them as lions. Even the pink hexagon, on the right margin, is classified as a lion as it is on the right-side, regardless of being on the margin. Margins are only deployed during training to optimize hyperplane positioning and are unused during testing or applications. SVM optimizes the hyperplane in training via margins to solve the optimization problem; hence, margins play no role in classifying new instances during testing. Hyperplanes take diverse shapes based on dataset and feature count. With one feature, they are points, e.g., grading students as pass/fail. Two features yield lines or shapes, three form planes, and \(M\) features create an \(M\)-dimensional hyperplane. Formulas (1)-(5) and Figure 5 depict such variations, showcasing blue and red circles representing classes, with the hyperplane depicted as a brown line or circle, as shown in Figure 6, which also depicts a three-dimensional hyperplane, distinct from the line and circle, where a hyperplane correlates with a dataset bearing three features, \(X\), \(Y\), and \(Z\) axes, when working with \(N\) features to allow the hyperplane to gain \(N\) dimensions, a concept easier to grasp when observing the one to the two and then finally to the three dimensions. Implementing an SVM involves five steps:  
1. Data Preparation: As SVM is supervised, labeled data are deployed for training. Instances must be associated with specific classes, where data collection takes various routes like downloading datasets from platforms like Kaggle [64] or customizing existing ones. 2. Feature Scaling: SVM gives weight to features based on values where scaling ensures fairness among features. While some features have a larger magnitude, maintaining equitable treatment prevents bias. Scaling methods like standardization and normalization are often employed. 3. Kernel Selection: SVM utilizes the kernel trick, mapping data to higher dimensions for easier classification. Kernels are of various types, suited to different data and applications. Optimal kernel choice impacts computational efficiency. 4. Training and Optimization: After the kernel is selected, training involves determining the hyperplane position. This necessitates solving an optimization problem, minimizing the cost function while considering margin and regularization factors.