## 5 Results and Discussion  
The accuracy, F1-score, MSE, and ROC curve measurements of the performance results are shown in Table 5, where the highest values of evaluation scores are marked in bold. If we did not use the F-OE model to predict the gas leakage level, the XGBoost algorithm showed the highest performance, with an accuracy rate of 94.99%, F1-score 95.53, and ROC 96.17% compared to the other machine learning algorithms of KNN, DT, RF, and NB. However, a factor analysis with OE (F-OE) model-based XGBoost and RF algorithms outperformed when using only the XGBoost algorithm. The proposed F-OE-XGBoost model achieved the highest accuracy of 95.14%, F1-score of 95.75%, MSE of 0.028, and AUC of 96.29%. Following this, the F-OE-RF model achieved the second-best accuracy rate of 95.09%, F1-score of 95.60%, MSE of 0.029, and AUC of 96.11%. The F-OE-NB model showed lower results compared to the other predictive models of the evaluation metrics. Table 5 shows that they were reduced from 17 dimensions to 7 dimensions by factor analysis, the accuracy of gas leak detection increased in all algorithms. Then indicates that the proposed factor analysis-based feature reduction method is suitable for predicting gas leak detection. We provided multi-class ROC curves for each compared model in the experimental dataset in Figure 6. As noted above, we proposed to find better model performance to predict XGBoost and KNN for this dataset. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Algorithms** & **Accuracy** & **F1** & **MSE** & **AUC** \\ \hline \multirow{4}{*}{7 features with OE} & F-OE-XGBoost & **95.141** & 0.957579 & 0.028226 & 96.29 \\  & F-OE -KNN & **95.018** & 0.952601 & 0.031551 & 95.88 \\  & F-OE -DT & 90.859 & 0.937716 & 0.041496 & 94.78 \\  & F-OE -RF & **95.093** & 0.956036 & 0.029196 & 96.11 \\  & F-OE -NB & 65.709 & 0.731945 & 0.173381 & 76.16 \\ \hline \multirow{4}{*}{7 features} & F-XGBoost & 94.993 & 0.955336 & 0.029722 & 96.17 \\  & F-KNN & 93.079 & 0.947657 & 0.034163 & 95.07 \\ \cline{1-1}  & F-DT & 56.678 & 0.678796 & 0.204025 & 72.82 \\ \cline{1-1}  & F-RF & 69.709 & 0.703196 & 0.179618 & 74.02 \\ \cline{1-1}  & F-NB & 70.916 & 0.762133 & 0.140000 & 76.74 \\ \hline \multirow{4}{*}{17 features} & XGBoost & 88.382 & 0.896736 & 0.065044 & 83.71 \\  & KNN & 84.902 & 0.850603 & 0.096150 & 79.39 \\ \cline{1-1}  & DT & 80.267 & 0.857235 & 0.095768 & 82.14 \\ \cline{1-1}  & RF & 88.702 & 0.896528 & 0.064185 & 82.86 \\ \cline{1-1}  & NB & 64.821 & 0.658825 & 0.207160 & 56.49 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Evaluation results of the compared algorithms on the experimental dataset (%). In addition, the ROC curve for each level of the experimental dataset in Figure 7 was determined. As mentioned above, we proposed to find a better model performance to predict medium and high-level classes for the experimental datasets. The F-OE model-based XGBoost shows the following higher ROC scores of 96.7% (low level), 96.1% (medium level), and 96.1% (high level) compared to the others for all class levels. Finally, we tuned the hyperparameter of XGBoost using the grid search infrastructure in Scikit-learn on the experimental dataset. Evaluating the effectiveness of the Bayesian hy  
Figure 6: Receiver operating characteristic curves of the algorithms compared to the F-OE method. Figure 7: Multi-class ROC curves of the compared F-OE algorithms for low, medium, and high levels: (**a**) ROC curve for the low-level class, (**b**) ROC curve for the medium-level class, and (**c**) ROC curve for the high-level class. perparameter optimization method on the XGB model increases the model's efficiency [17]. They then assessed values for the max depth between 1 and 12 (2, 4, 6, 8, 10, and 12). We plotted the relationship between each series of max depth values for the given n estimators in Figure 8. We have achieved the best result with the settings of n-estimators = 350 and max depth = 12.