## 4 The Proposed Approach and Its Application to the HFAVD Dataset
We selected the random forest algorithm for evaluation due to its superior results demonstrated in our previous research [2]. Figure 5 shows the F1-score for different threshold values obtained through experiments. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Participant Id** & **Ku** & **K** & **Au** \\ \hline
1 & 10–450 & 53.6–98.2 & 0.18–2.85 \\
2 & 16–225 & 56.8–95.8 & 0.39–2.71 \\
3 & 14–450 & 45.7–98.4 & 0.00–2.87 \\
4 & 12–300 & 57.6–97.1 & 0.45–2.81 \\
5 & 9–180 & 53.3–95.8 & 0.18–2.70 \\
6 & 11–900 & 63.6–100.0 & 0.59–3.13 \\
7 & 1–300 & 33.0–97.5 & 0.00–2.83 \\
8 & 12–900 & 57.3–100.0 & 0.31–2.99 \\
9 & 3–12 & 36.3–69.7 & 0.00–0.83 \\
10 & 5–90 & 45.5–91.1 & 0.00–2.45 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Mental performance (Au), attention (K), and the stability of concentration of attention (Ku) for each participant in the dataset. Moreover, we recognized that vital signs vary significantly between individuals. To address this, we meticulously normalized these metrics before incorporating them into our predictive models. This normalization allowed our models to accurately account for individual differences, thereby providing more reliable predictions of fatigue. We used the min-max normalization function shown in Equation (4). \[X^{\prime}=\frac{X-X_{\text{min}}}{X_{\text{max}}-X_{\text{min}}} \tag{4}\]  
where the following apply:  
* \(X\) is the original vital sign value. * \(X^{\prime}\) is the normalized vital sign value. * \(X_{\text{min}}\) is the minimum value of the vital sign for the participant. Figure 4: The relationship between the mental performance and the inverse of fatigue (red dotted line denotes an example threshold value separating fatigued and not fatigued states). Figure 5: The relationship between the threshold and the F1-score. * \(X_{\text{max}}\) is the maximum value of the vital sign for the participant. As we can see from the figure, there is a threshold value, 0.38, which achieves the best F1-score. To predict the fatigue state, several methods were evaluated, including Support Vector Classifier (SVC), logistic regression, Multi-Layer Perceptron (MLP), decision tree, XGBoost, and random forest. Each method has distinct characteristics, which are shown in Table 5.  
The hyperparameters for each model were fine-tuned by using grid search to optimize performance. For SVC, we used a Radial Basis Function (RBF) kernel with a regularization parameter C = 1.0 and the kernel coefficient set to'scale'. In logistic regression, we applied an L2 (Ridge) penalty with a regularization strength C = 0.001 and used the 'lfbgs' solver for optimization. The MLP classifier was configured with two hidden layers, with each using a linear activation function. The ReLU function was applied as the activation function for the neurons, [PERSON] was selected as the solver, and the learning rate was set to \(1\times 10^{-3}\). For the decision tree, the Gini impurity was used as the splitting criterion, with a maximum tree depth of 20, a minimum of two samples required per leaf, and a minimum of two samples required to split a node. In the XGBoost model, the 'gbtree' booster was utilized. Key hyperparameters included a learning rate of 0.1, a maximum depth of 3, a minimum loss reduction (gamma) of 2, a feature subsample ratio (colsample_bytree) of 0.8, and 100 estimators (trees). The random forest classifier also employed 100 estimators with the Gini impurity criterion. It had a maximum tree depth of 20, used 'log2' as the maximum number of features to consider when splitting, and required a minimum of two samples to split a node. The environment used for these experiments was Python, with scikit-learn employed for SVC, logistic regression, MLP, decision tree, and random forest, while the XGBoost library was used for the XGBoost method. This setup ensures that the characteristics of each classification method are clearly presented and understood. Table 5 shows the performance of the models using the threshold of 0.38 to detect the fatigue state based on the mental performance.