## 3 Materials and Methods
### Clustering Methods Used in the Research  
The following section provides an in-depth overview of the clustering algorithms that were employed to analyze the dataset under investigation. Clustering is a fundamental technique in unsupervised machine learning. It offers valuable insights into data's inherent structure and relationships by grouping similar objects into clusters based on their features. Selecting appropriate clustering algorithms is crucial for obtaining accurate and meaningful results. Each method has its strengths and weaknesses depending on the data's specific characteristics and the analysis's objectives. In this research, we have carefully chosen a diverse set of clustering algorithms, including hierarchical, partitioning, density-based, and model-based methods, to provide a comprehensive understanding of the underlying patterns in the data. Each clustering method offers a unique perspective on the data organization. By comparing their results, we aimed to derive robust conclusions and minimize potential biases associated with any algorithm [60]. This section will outline the principles and rationale behind each clustering method used in the study, discuss their respective strengths and limitations, and provide a detailed explanation of their implementation within the context of this research. Furthermore, we will describe the process of selecting the optimal number of clusters and present the unsupervised evaluation metrics employed to assess the quality of the clustering results obtained from each algorithm. The main data clustering techniques used in this study are discussed below. K-means clustering is a widely used unsupervised learning technique that aims to partition unlabeled data into distinct clusters based on their inherent features [61]. K-means clustering operates by iteratively assigning data points to a predefined number of cluster centroids based on the minimization of within-cluster distances, typically using Euclidean distance as the similarity measure. The algorithm initializes by selecting random or strategically placed centroids. It then iteratively refines their positions until convergence, resulting in compact and well-separated clusters. One of the main advantages of K-means is its simplicity and ease of implementation, which makes it computationally efficient and suitable for large datasets. However, the algorithm has limitations, such as sensitivity to the initial centroid positions and the requirement to specify the number of clusters a priori, which may not always be known or easily determined [62]. Additionally, K-means is predominantly suited for detecting spherical and equally sized clusters and may struggle with more complex data. Recent advancements in this field have expanded its applicability to various domains, including text analytics. For instance, K-means has been employed in document clustering, grouping similar textual information, and enhancing information retrieval efficiency. DBSCAN (Density-Based Spatial Clustering of Applications with Noise) is a density-based clustering algorithm that identifies clusters by grouping data points that are tightly packed based on a specified distance metric and density threshold [63] ([PERSON] et al., 1996). This approach allows DBSCAN to effectively manage clusters of arbitrary shapes and noise in the data, which is a significant advantage over traditional partitioning methods such as K-means. However, DBSCAN is sensitive to its hyperparameters, namely the neighborhood radius (Eps), and the minimum number of points required to form a dense region (MinPts), which can be challenging to determine a priori [63]. HDBSCAN (hierarchical density-basedspatial clustering of applications with noise) is an extension of DBSCAN that addresses some of its limitations by incorporating a hierarchical clustering approach [64].