## 3 Methodology: Proposed SybilSocNet Algorithm
### ML Terminologies and Methodologies Applied in This Study
#### 3.1.2 Supervised Learning  
ML algorithms are classified based on training methods, with one type being supervised learning, where algorithms learn by mapping inputs to outputs via a labeled dataset containing input-output pairs [51], i.e., the algorithm is trained on instances with known labels. Supervised learning effectiveness arises from having correct target outputs, while the algorithm continually refines its output by calculating a value from a loss function, a value that guides adjustments to the model's weights for achieving the desired output. For instance, when predicting car prices via feature data, e.g., previous prices, model number, brand, mileage, and accident history, an algorithm predicts the car value via inputs like model, make, and mileage. Supervised learning, with broad applications like image recognition, natural language processing (NLP), and speech recognition, were employed in this study in supervised ML to distinguish Sybil from legitimate social media Twitter accounts via two key types: classification and regression. A classification problem concerns categorizing data into specified classes, e.g., classifying animal images into cats or dogs, or segregating individuals by age, either 20-30 or greater than 30. Such exemplary classification ML algorithm tasks determine the group where an instance belongs. Common classification algorithms are decision trees, support vector machines, and random forests, which are trained on labeled data to classify new data but the prerequisite is first choosing the right algorithm relying on factors like dataset size, training methods, and desired accuracy. [PERSON] et al. [52] tackles classification problems via a naive Bayes classifier to distinguish spam from legitimate emails through automated filters for classifying inbox emails, to enhance user experience by excluding unwanted content. Unlike classification, where the ML algorithm predicts a predetermined class, regression predicts a value, e.g., car selling price or a person's due date. Unlike supervised learning, unsupervised learning omits labeled data for training, instead analyzing unlabeled data, revealing patterns and relationships, being applicable in clustering and anomaly detection [53]. The K-nearest neighbors (KNN) algorithm, a flexible supervised method, learns from labeled data to predict labels for unlabeled instances. It memorizes patterns during training, then utilizes them for predicting new instance labels, serving both classification and regression tasks based on its training.To label a new instance, KNN compares memorized instances and assigns labels using similarities [54]. Next, this study illustrates real-world KNN functions for predicting housing price trends for investors' decision making. Initially, when employing the KNN algorithm as a classifier, classes are distinguished, and the model's accuracy is assessed via labeled instances by splitting the dataset for training and testing using various techniques, e.g., cross-validation, including resubstitution validation, K-fold cross-validation, and repeated K-fold cross-validation, each with its strengths and applications. Next, the KNN algorithm determines the number of neighbors (K) for predicting class, influencing accuracy. Optimal K selection balances pattern detection and sensitivity. Next, compute distances between the instance and its neighbors. The closest K neighbors' classes decide the predicted class using distance metrics (e.g., Euclidean, Manhattan, Minkowski). Refer to Formula (1) for these methods [55]. Another distance-measuring method is cosine similarity, depicted in Formula (2), commonly used in text retrieval, as discussed by [PERSON] [15]. Additionally, the KNN equation employs diverse distance formulas from [PERSON] [18] to introduce the Minkowski distance Formula (3), the chi formula (Formula (4)), and the correlation equation (Formula (5)) by [PERSON] and [PERSON] [56], which constitute distinct distance metrics for KNN's neighbor distance calculation.