## 3 Methods
### Visual Analysis  
Conducting data classifications with different machine learning algorithms is valuable for assessing their effectiveness in distinguishing between \"normal\" and \"abnormal\". However, the clarity in differentiating between them is hindered by the imbalanced data. Imbalanced data may cause challenges in comprehending the performance of a classification model due to its inherent unreliability. To address this issue, we considered leveraging visualization techniques to represent the extracted features by mapping them into visual glyphs. Visual representations can help in understanding the patterns and structures of the data by revealing underlying patterns. Since the data utilized in this study consist of numerous variables, dimension reduction is applied to show the data in a lower-dimensional space (i.e., 2D space). In the visualization domain, various dimension reduction techniques have been employed for presenting high-dimensional data, including PCA, LDA, MDS (multi-dimensional scaling), t-SNE (t-distributed stochastic neighbor embedding), UMAP (Uniform Manifold Approximation and Projection), and others [46]. Among them, t-SNE and UMAP have been broadly used recently by researchers in representing data because they show a better separation of the classes than others. However, these methods come with computational costs to approximate the optimal positions. Therefore, we considered using PCA to determine the points representing the high-dimensional data. It computes \begin{table}
\begin{tabular}{c c} \hline \hline
**Region** & **Channel Information** \\ \hline Frontal & FP1, FP2, F3,F4, F7, F8, AF3, Fz, Fpz \\ \hline Temporal & T3, T4, T5, T6, T7, T8 \\ \hline Central & C3, C4, CZ, C5, C1, C2 \\ \hline Parietal & P3, Pz, P4, \\ \hline Occipital & O1, O2, Oz \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Five brain regions are defined and analyzed. Each region consists of multiple relevant channels to initiate the region-based analysis. eigenvectors and eigenvalues to identify multiple principal components. By utilizing the 1 st and 2 nd principal components, the data can be effectively represented in a 2D space [47]. We also employed parallel coordinates visualization [48] to represent all data instances. It generates polylines through vertically arranged variables (i.e., parallel axes), representing individual instances. Despite its effectiveness in presenting multivariate data, researchers have proposed numerous variations of parallel coordinates visualization [49; 50]. However, parallel coordinates visualization has a major limitation when handling large data instances, occurring a visual cluttering problem where multiple polylines overlap. To address this problem, researchers considered reducing the number of polylines or rearranging (or reordering) the axes of the parallel coordinates. Since we utilized the parallel coordinates visualization to understand the patterns between classes, we did not consider addressing the visual cluttering problem in this study. Instead, we considered showing data distribution in each axis because it helps users understand clusters in each group (e.g., normal vs. abnormal). To represent data distributions in each variable, angular histograms [51] were generated to illustrate the density and slopes of underlying polylines overlaid onto the parallel coordinates. Angular histogram is a technique that presents the frequency distribution of underlying data within each parallel axis by measuring the frequency of the data and the directional information of polylines in each axis. Figure 1 shows an example of applying angular histograms to parallel coordinates. The histogram highlights density using different colors (red for high density and green for low density) based on the measured distributions. To measure the distributions, various statistical approaches have been proposed to determine an appropriate bin size for histograms [52]. However, traditional histograms only present univariate data.