## 3 Manifold Dimension Transformation of Raman Spectra of Oil-Paper Insulation
### XGBoost Optimization of the Raman Spectra after Oil-Paper Insulation Aging  
After the feature extraction, 175 Raman spectrum samples were divided into training and test sets in a ratio of 7:3. The dimensions of the samples were sequentially modified \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Hyperparameters**} & **Hyperparameter Selection Range** & \
\begin{tabular}{c} **Hyperparameter** \\ **Optimization Values** \\ **(Ten Categories)** \\ \end{tabular} &
\begin{tabular}{c} **Hyperparameter** \\ **Optimization Values** \\ **(Four Categories)** \\ \end{tabular} \\ \hline Number of decision & (0, 100) & 94.00 & 96.00 \\ Maximum tree depth & (1, 10) & 7.00 & 6.00 \\ Subsample & (0.5, 1) & 0.91 & 0.86 \\ gamma & (0, 1.0) & 0.01 & 0.01 \\ Learning\_rate & (0.01, 1) & 0.09 & 0.07 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Bayesian optimization hyperparameter table of PCA feature-extraction results. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Hyperparameters**} & **Hyperparameter Selection Range** & \
\begin{tabular}{c} **Hyperparameter** \\ **Optimization Values** \\ **(Ten Categories)** \\ \end{tabular} &
\begin{tabular}{c} **Hyperparameter** \\ **Optimization Values** \\ **(Four Categories)** \\ \end{tabular} \\ \hline Number of decision & (0, 100) & 97.00 & 95.00 \\ Maximum tree depth & (1, 10) & 8.00 & 8.00 \\ Subsample & (0.5, 1) & 0.92 & 0.66 \\ gamma & (0, 1.0) & 0.01 & 0.01 \\ Learning\_rate & (0.01, 1) & 0.10 & 0.12 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Bayesian optimization hyperparameter table of Isomap feature-extraction results. Figure 13: Discrimination accuracy after changing \(k\) value. (**a**) Four categories; (**b**) ten categories. and substituted into the BO-XGBoost model. The stacked plot illustrating the relationship between the sample dimensions in the test set and the accuracy of the classification is presented in Figure 14.  
The random seed is set to 200 to partition the Raman spectroscopy samples into training and testing sets. It can be observed that the accuracy of Isomap feature extraction decreased as the dimensions increased. The highest accuracy for the four-class classification was achieved at five dimensions, while corresponding to three dimensions for the ten-class classification. On the other hand, the accuracy of PCA increased with the increase in feature dimensions, and the best accuracy for both the four-class and ten-class classifications was enriched at seven dimensions. Therefore, a dimensionality of seven was considered optimal for PCA. In the case of MDS feature extraction, there was no clear relationship between accuracy and dimensionality. For the ten-class classification, each Raman spectroscopy sample was reduced to three, seven, and three dimensions using MDS, PCA, and Isomap techniques, respectively. The discriminative results on the samples after feature extraction according to the three algorithms are shown in Figure 15. Based on the plots, only 1 sample from the fourth stage and 1 sample from the seventh stage of the Raman spectroscopy dataset were misclassified after Isomap feature extraction, while the remaining 51 samples were correctly classified. After PCA feature extraction, five Raman spectroscopy samples from aging stages 1, 4, 5, and 7 were misclassified. After MDS feature extraction, six Raman spectroscopy samples from aging stages 1, 3, 4, 7, and 8 were misclassified. In the same manner, 175 samples were subjected to the four-class classification, as indicated in Table 1, and the final classification data are presented in Figure 16.  
Figure 14: The relative change in discriminant accuracy with dimension. Figure 15: Ten class discriminant maps revealing (**a**) MDS+XGBoost discrimination results; (**b**) PCA+XGBoost discrimination results; and (**c**) Isomap+XGBoost discrimination results. As seen from Figure 11, the Isomap algorithm yielded the highest accuracy of the classification results after feature extraction.