## 3 Manifold Dimension Transformation of Raman Spectra of Oil-Paper Insulation
### Final Discrimination Results  
The accuracy rates of the four and ten categories of the samples before and after feature extraction were further compared according to the formula below:  
\[ACC=\frac{TP}{TP+FP}, \tag{24}\]  
where _TP_ is the number of correctly predicted category samples and _FP_ is the number of incorrectly predicted category samples.  
In order to further analyze the discriminative ability of the model on different training sets and test samples, and to prevent overfitting of the discriminative model, 10-fold cross-validation was performed. The final average discriminative accuracy and the standard deviation of accuracy are shown in Table 8.  
The statistical results of the discriminative accuracy indicate that, except for a slight decrease in the average discriminative accuracy of the four-class classification after applying the MDS algorithm for feature extraction, the remaining feature-extraction algorithms consistently achieve higher average discriminative accuracy compared to the results without feature extraction. Among the three feature-extraction algorithms, the Isomap algorithm demonstrates the greatest improvement in discriminative accuracy. After feature extraction, the classification accuracy for the four aging states increases from 89.5% to 97.0%, and the accuracy for the ten classes increases from 85.9% to 95.1%.  
These results indicated that employing the Isomap algorithm for feature extraction enabled one to reduce the Raman data dimensionality after oil-paper insulation aging  
Figure 16: Four class discriminant maps revealing (**a**) MDS+XGBoost discrimination results; (**b**) PCA+XGBoost discrimination results; and (**c**) Isomap+XGBoost discrimination results.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Feature-** \\ **Extraction** \\ **Method** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Average** \\ **Discrimination** \\ **(Four** \\ **Categories**) \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Accuracy** \\ **Standard** \\ **Deviation (Four** \\ **Categories**) \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Accuracy** \\ **Standard** \\ **Deviation (Four** \\ **Categories**) \\ \end{tabular} } \\ \hline Without feature & \multirow{2}{*}{89.5} & \multirow{2}{*}{85.9} & \multirow{2}{*}{2.54} & \multirow{2}{*}{2.72} \\ extraction/\% & & & & \\ PCA feature & \multirow{2}{*}{90.2} & \multirow{2}{*}{90.9} & \multirow{2}{*}{2.79} & \multirow{2}{*}{1.98} \\ extraction/\% & & & & \\ MDS feature & \multirow{2}{*}{88.5} & \multirow{2}{*}{88.7} & \multirow{2}{*}{3.61} & \multirow{2}{*}{2.35} \\ extraction/\% & & & & \\ Isomap feature & \multirow{2}{*}{97.0} & \multirow{2}{*}{95.1} & \multirow{2}{*}{2.50} & \multirow{2}{*}{1.80} \\ extraction/\% & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 8: Accuracy comparison of different feature-extraction methods.  
and to improve differentiation between various categories, thereby leading to a notable enhancement in classification accuracy. This contributes to the improvement in the accuracy of aging state discrimination.