## 4 Results and Analysis
### Prediction Results
#### 4.3.2 Prediction Results Based on Relatively Balanced Training Dataset  
In this section, all classifiers are trained on the relatively balanced training data based on SMOTE. Table 5 showcases the hyperparameter optimization outcomes for each classifier. Table 6 shows the PRE and REC values of each classifier on the relatively balanced dataset. Comparing Tables 3 and 5, it can be seen that all classifiers have closer PRE and REC values on the relatively balanced dataset. Taking the SVM classifier as an example, on the imbalanced dataset, the PRE 5-fold CV mean value and REC 5-fold CV mean value are 0.868 and 0.975, respectively, while on the relatively balanced dataset, both values are 0.913 and 0.943, respectively. It is worth noting that the PRE 5-fold CV mean value and REC 5-fold CV mean value of the ensemble classifiers, including the proposed stacking ensemble classifier, XGBoost, GBDT, and RF, show relatively little change. This phenomenon also indicates that compared to classical classifiers, ensemble classifiers have more advantages on imbalanced datasets compared with individual classifiers. \begin{table}
\begin{tabular}{c c c c} \hline
**Classifier** & _AUC_ & _PRE_ & _REC_ \\ \hline SVM & 0.945 \(\pm\) 0.0417 & 0.868 \(\pm\) 0.0512 & 0.975 \(\pm\) 0.0273 \\ KNN & 0.897 \(\pm\) 0.0916 & 0.842 \(\pm\) 0.0314 & 0.991 \(\pm\) 0.0149 \\ DT & 0.890 \(\pm\) 0.0958 & 0.922 \(\pm\) 0.0509 & 0.901 \(\pm\) 0.0605 \\ LR & 0.932 \(\pm\) 0.0774 & 0.839 \(\pm\) 0.0324 & 0.997 \(\pm\) 0.0072 \\ GBDT & 0.934 \(\pm\) 0.0778 & 0.922 \(\pm\) 0.0538 & 0.943 \(\pm\) 0.0515 \\ RF & 0.956 \(\pm\) 0.0483 & 0.907 \(\pm\) 0.0589 & 0.967 \(\pm\) 0.0479 \\ XGBoost & 0.950 \(\pm\) 0.0550 & 0.922 \(\pm\) 0.0522 & 0.957 \(\pm\) 0.0383 \\ Stacking & 0.958 \(\pm\) 0.0735 & 0.941 \(\pm\) 0.0559 & 0.957 \(\pm\) 0.0257 \\ \hline \end{tabular}
\end{table} 
Table 4: Prediction results of each classifier based on imbalanced training dataset. Figure 14: Prediction results of each classifier based on imbalanced training dataset: (a) _acc_; (b) \(F1\); (c) _kappa_. In order to further analyze the impact of imbalanced datasets on classifiers, the metrics introduced in Section 2 were calculated, including accuracy, AUC, F1, and kappa. Tables 7-10 show the _acc_, _AUC_, _F1_, _kappa_, and mean variation between the imbalanced and relatively balanced datasets. The following can be observed from the tables:  
* For _acc_, all classifiers improved differently on the relatively balanced dataset. The mean accuracy of SVM, KNN, DT, LR, GBDT, RF, XGBoost, and the stacking ensemble classifier increased by 1.5%, 2.6%, 1.8%, 2.3%, 0.9%, 0.8%, 0.6%, and 1.1%, respectively. It is worth noting that the accuracy increase in the ensemble classifiers represented by the stacking ensemble classifier is lower than that of the individual classifiers, which also indicates that the ensemble classifiers have advantages in processing imbalanced datasets. In addition, the accuracy increase in the stacking ensemble classifier is greater than that of the GBDT, RF, and XGBoost ensemble classifiers. This phenomenon can be attributed to the accuracy increase in the base classifiers. The use of SMOTE has led to a relatively balanced training dataset, resulting in improved performance for individual classifiers. The moderately balanced dataset reduces the risk of classifier overfitting and ultimately enhances the evaluation metrics for the classifier. Due to the improved performance of base classifiers, the final stacking ensemble model also shows improvement. * For _AUC_, it can be found that, with the exception of the RF (a decrease of 0.005) and XGBoost (a decrease of 0.006) classifiers, the AUC values of all other classifiers increased. Among them, the SVM classifier has the highest improvement of 0.012, and DT showed the lowest improvement of 0.003. * It can be found that all classifiers have varying degrees of increases in \(F1\). Among them, KNN and DT have the largest increase, at 0.011, and the stacking ensemble classifier shows the smallest increase of 0.003.