## 3 Materials and Methods
### Dimensionality Reduction Methods  
Vectorization of textual data often results in extremely large matrices. In the case of sentence transformers, the resulting matrix is Nx364. In contrast, the TF-IDF matrix depends on how many different words are in the data and which N-gram is used. Data dimensionality reduction plays a particularly significant role in data analysis and various machine learning techniques by reducing high-dimensional datasets to low-dimensional datasets that contain only the most valuable information and relationships. Large datasets can be challenging to work with as they often contain noise, redundancy, and sparsity, making it difficult to identify patterns and relationships in the data. When performing data clustering, a particularly enormous number of dimensions is not desirable if these dimensions do not provide additional information. Data dimensionality reduction is an important preprocessing step prior to data clustering, as it helps overcome the challenges many dimensions face. This phenomenon is often known as the \"curse of dimensionality\" ([PERSON] et al., 2014). As sparsity in high-dimensional spaces increases, many dimensions can lead to the overfitting and poor clustering of the results. With the utilization of data dimensionality reduction, it has been noticeable that better data clustering results are obtained, and such results are much easier to interpret ([PERSON] et al., 2014). Data dimensionality reduction techniques have also been well used to reduce noise in data ([PERSON] et al., 2014), or detect outliers in the data ([PERSON] et al., 2014), and improve the accuracy and generalization of the models being developed ([PERSON] et al., 2014). Data dimensionalities reduction methods such as principal component analysis (PCA), t-distributed stochastic neighbor embedding (t-SNE), and uniform manifold approximation and projection (UMAP) transform the original high-dimensional data into smaller-dimensional data, while also retaining as much as possible, more similar data structures and relationships between the individual data points ([PERSON] et al., 2014). These data dimensionality reduction techniques allow clustering methods such as k-means and DBSCAN to identify clusters in the data more efficiently. Moreover, data dimensionality reduction methods significantly reduce computational complexity and memory requirements for clustering methods, thus enablingthem to perform actions with larger datasets. However, it is important to note that data dimensionality reduction methods also have their disadvantages. One is that a certain amount of information can be lost when the dimensionality is reduced [50]. The main data dimensionality reduction techniques used in this study are briefly discussed below. One of the most widely used and widely known data dimensionality reduction techniques is principal component analysis (PCA). The principal component analysis is a linear method that projects data into a space of smaller dimensions to maximize variance and, at the same time, minimize information loss. PCA identifies and extracts the principal components, which are orthogonal linear combinations of the original variables, capturing the maximum variance in the data while minimizing information loss [51]. The principal components are ranked according to their variance. Hence, the first principal component captures the largest variance, the second principal component the second largest variance, and so on. By retaining only a few principal components with a higher variance, PCA can effectively reduce the dimensionality of the data while retaining most of the information. PCA has been successfully applied in various domains, including image processing, bioinformatics, and finance, for feature extraction, data compression, visualization, and noise reduction [52; 53].