## 4 Experimental Results and Analysis
### Analysis of Experimental Results
#### 4.3.2 Wine Quality-White Data Set  
According to the steps of optimized BT-MTS, fitness function values can be obtained, as shown in Table 6, from which it can be seen that the fitness function value of class 5 is the smallest. Therefore, this class should be used as the left subtree of the root node to construct the MS. After removing this class, the fitness values of the remaining categories are calculated. Finally, the classification order of the data set is category 5, 6, 3, 4, 8, 9, and 7. The threshold values for MTS1-MTS6 are 0.8429, 1.7956,2.7071, 1.3308, 2.6967, and 2.0202. The feature selection results are shown in Table 7. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \(c_{3}\) & \(c_{4}\) & \(c_{5}\) & \(c_{6}\) & \(c_{7}\) & \(c_{8}\) & \(c_{9}\) \\ \hline Stage 1 & \(-\)26,928 & \(-\)260 & \(-\)2,110,498 & \(-\)6114 & \(-\)128,959 & \(-\)141,914 & \(-\)2,015,752 \\ Stage 2 & \(-\)10,899 & \(-\)10,439 & / & \(-\)42,569 & \(-\)11,102 & \(-\)3185 & \(-\)1208 \\ Stage 3 & \(-\)487,094 & \(-\)60,492 & / & / & \(-\)54,679 & \(-\)233,864 & \(-\)1835 \\ Stage 4 & / & \(-\)676,814 & / & / & \(-\)201 & \(-\)16,650 & \(-\)21,435 \\ Stage 5 & / & / & / & / & \(-\)764 & \(-\)106,886 & \(-\)27,410 \\ Stage 6 & / & / & / & / & \(-\)115,434 & & \(-\)158,500 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Values of fitness function at different stages of the Wine quality-white data set. Figure 4: Comparison of DRR of the balance data set. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multirow{2}{*}{**Parameter Set**} & \multicolumn{5}{c}{**Evaluation Index**} \\ \cline{3-6}  & & & **Acuracy** & **Macro-F1** &
\begin{tabular}{c} **Kappa** \\ **Coefficient** \\ \end{tabular} & **CBA** & **Cost** \\ \hline Optimized BT-MTS & \multicolumn{2}{c}{Joint optimization model} & 0.8880 & 0.7939 & 0.8102 & 0.7473 & 31.7489 \\ BT-MTS & \multicolumn{2}{c}{Use SNR\({}_{\text{18}}\) gain value to select feature variables, PTM} & 0.7680 & 0.6590 & 0.6151 & 0.5866 & 114.3063 \\ RF & \multicolumn{2}{c}{Ntree = 50, NumPredictors/ToSample = 2} & 0.8560 & 0.6076 & 0.7411 & 0.5873 & 74.0410 \\ FCBF-SVM & \multicolumn{2}{c}{BoxConstraint = 3.0625, KernelScale = 0.0625} & 0.7600 & 0.5321 & 0.5622 & 0.5074 & 88.5306 \\ SMOTE-KNN & \multicolumn{2}{c}{K = 4} & 0.7500 & 0.7549 & 0.6223 & 0.6970 & 83.1721 \\ BPNN & \multicolumn{2}{c}{Hiddensize = 4} & 0.8960 & 0.8186 & 0.8238 & 0.7695 & 26.0712 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of the classification results of the balance data set. According to the BT-MTS method, the classification sequence is category 5, 9, 8, 3, 6, 7, and 4. The MTS classifiers were thus trained in sequence, resulting in the feature variable selection results in Table 8. The threshold values for MTS1-MTS6 are 1.6811, 0.6667, 1.5734, 1.2118, 3.3241, and 1.7486, respectively. The DRR of the optimized BT-MTS and BT-MTS are shown in Figure 5, and it can be seen that the dimensionality reduction performance of this paper's method is better than that of BT-MTS. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & \(x_{1}\) & \(x_{2}\) & \(x_{3}\) & \(x_{4}\) & \(x_{5}\) & \(x_{6}\) & \(x_{7}\) & \(x_{8}\) & \(x_{9}\) & \(x_{10}\) & \(x_{11}\) \\ \hline MTS1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 \\ MTS2 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ MTS3 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 1 \\ MTS4 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ MTS5 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 \\ MTS6 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 \\ \hline \hline \end{tabular} Note. “1”means using the variable, “0” means not using the variable.  
\end{table} 
Table 7: Feature variable selection results of Optimized BT-MTS of the Wine quality-white data set. Figure 5: Comparison of DRR of the Wine quality-white data set.