## 3 Materials and Methods
### Dimensionality Reduction Methods
Recent advances in PCA include incorporating regularization techniques, such as sparse PCA and elastic net PCA, which add constraints to improve the interpretability and robustness of the model, particularly in high-dimensional data with multicollinearity issues [54]. Despite its advantages, PCA has certain limitations, such that it assumes linearity in the data, which may not always be appropriate, especially when the data exhibits complex nonlinear structures. Another data dimensionality reduction method that, in contrast to principal component analysis, is not linear, is t-distributed stochastic neighbor embedding (t-SNE). This method has been widely used due to its ability to maintain local and global relationships in high-dimensionality reductions, thus maintaining exceptionally good data visualization and interpretation [55]. This method has gained much attention recently due to its ability to effectively visualize large-dimensional data by representing it in smaller dimensions [56]. The t-SNE algorithm achieves this by converting high-dimensional Euclidean distances into conditional probabilities, representing similarities between data points. Then, a gradient descent optimization method minimizes the divergence between these probabilities across dimensions [57]. Researchers have proposed efficient approximations, such as the Barnes-Hut t-SNE, which allows the algorithm to manage large datasets while maintaining its effectiveness in preserving local structures. T-SNE has been widely applied across various scientific domains, including single-cell analysis, bioinformatics, and computer vision. Despite its success, certain limitations of t-SNE have been identified, such as sensitivity to initial conditions and hyperparameters, slow convergence, and the presence of local optima [56]. Uniform manifold approximation and projection (UMAP) is a newer data dimensionality reduction method. Similar to t-SNE, it is nonlinear, and can maintain local and global relationships. Data dimensionality reduction improves data visualization and interpretation [49]. UMAP is built on the foundations of multivariate learning and topological data analysis, using concepts such as simple fuzzy sets to model the underlying geometry of the data [58]. UMAP creates fuzzy topological representations of high-dimensional data and projects them into a lower-dimensional space. The resulting projection preserves the local structure of the data, meaning that nearby points in high-dimensional space are also close to each other in the low-dimensional projection. UMAP is similar to other dimensionality reduction methods, such as t-SNE and PCA, but has several advantages over these methods. For example, UMAP is generally faster and more scalable than t-SNE and can handle larger datasets. In addition, UMAP can be used with various distance metrics, including non-Euclidean metrics that allow for capturing complex data relationships. UMAP's preservation of local and global structures facilitates data visualization and interpretation. It is suitable for various applications, including single-cell RNA-seq data analysis [58], image classification, and natural language processing tasks [59]. In addition,UMAP has shown faster execution times than t-SNE, making it more suitable for large-scale datasets [49]. Recent advances in UMAP include the development of supervised and semi-supervised variants that incorporate label information into the dimensionality reduction process, resulting in improved class separation and more meaningful embeddings. Despite its advantages, UMAP can exhibit some limitations, especially in cases where assumptions about the underlying data collector do not hold, or when the data show high noise levels. In such situations, alternative dimensionality reduction methods may be better. In this work, we assessed different dimensionality reduction methods listed in this section and different method performances presented in the results sections.