## 3 Methodology
### Evaluation Metrics  
The evaluation metrics employed in this study are accuracy, precision, recall (sensitivity), the F1 score, and ROC curves. These metrics offer critical insight into the performance of the machine learning models applied to the depression detection task using EEG data. The metrics are computed for each model using 5-fold cross-validation, with the Stratified-KFold method ensuring that the class distribution was preserved across different subsets of data for consistent and reliable evaluation [55].  
The model training process involved splitting the dataset into five equal-sized folds. In each iteration, one fold was used as the validation set while the other four folds were used for training, ensuring that each data point was used for both training and validation exactly once. This process was repeated five times, with the final performance metrics averaged across all iterations to provide a robust estimate of model performance. This cross-validation approach helped reduce the risk of overfitting and ensured a more generalized assessment across different subsets of the data.  
Preprocessing steps included normalizing the EEG data to standardize feature values. For each training fold, feature selection methods (e.g., SVM-RFE, Elastic Net) were applied to avoid data leakage. The selected feature set was then used for training the classifiers, whose hyperparameters were optimized using GridSearchCV, as outlined in Section 3.3.  
* Accuracy is the percentage of correctly classified data points (both true positives and true negatives) out of the total number of instances [56]: \[Accuracy=\frac{\text{TP}+\text{TN}}{\text{TP}+\text{TN}+\text{FP}+\text{FN}}\] where TP = True Positives, TN = True Negatives, FP = False Positives, FN = False Negatives.
* Precision measures the accuracy of positive predictions by evaluating the percentage of correct positive predictions relative to all predicted positives. It is calculated as the ratio of true positives to the sum of true positives and false positives: \[Precision=\frac{\text{TP}}{\text{TP}+\text{FP}}\]
* Recall, also known as sensitivity or true positive rate, measures the proportion of actual positive instances that were correctly predicted by the model. It represents the percentage of actual positive data points that are correctly predicted: \[Recall=\frac{\text{TP}}{\text{TP}+\text{FN}}\]
* F1 score is the harmonic mean of precision and recall, providing a balanced measure of model performance. The F1 score is defined as: \[F1=\frac{2\cdot\text{Precision}\cdot\text{Recall}}{\text{Precision}+\text{ Recall}}\]ROC curves plot the true positive rate against the false positive rate by adjusting the classifier's threshold or score for class membership. The area under the ROC curve (AUC) is a single metric that is used for assessing and comparing classifier performance. It represents the probability that a classifier will rank a randomly chosen positive instance higher than a randomly chosen negative instance. AUC values range from 0 to 1, with a higher value indicating better performance across all possible thresholds. ROC curves are widely used to visually compare the performance of binary classifiers.  
These metrics are particularly useful in binary classification tasks, where the goal is to differentiate between two classes (e.g., depression vs. non-depression). They provide a comprehensive assessment of model performance, considering both correct and incorrect predictions and highlighting trade-offs between precision and recall [56].