## 3 Results and Discussion
### THz Data Analysis  
A pairwise comparison of THz spectra for experimental and corresponding control groups is shown in Figure 7. The non-overlapping region of 0.5-0.8 THz appeared promising for further analysis. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Experimental Group** & **Days after Injection of U87 Cells** & **U87 Glioblastoma Volume, mm3** \\ \hline U87-1 & 7 & 2.6 \(\pm\) 0.4 \\ \hline U87-2 & 14 & 10.6 \(\pm\) 1.8 \\ \hline U87-3 & 21 & 89.6 \(\pm\) 11.5 [1] \\ \hline \hline \end{tabular} \({}^{1}\)_p \(<\) 0.001._  
\end{table} 
Table 1: U87 glioblastoma volume (mm3). Values are presented as means \(\pm\) standard error of the mean. Figure 7: _Cont._  
Table 2 contains the results of the IF method applied for outlier removal. Figure 7: Mean THz spectra and scatter values for (**a**) experimental group 1, (**b**) group 2, (**c**) group 3, and the corresponding control groups. The highest percentage of outliers was observed in the THz data for the third week of the experiment. The number of outliers did not correlate with the glioma stage. After outlier removal, the data were standardized by subtracting the mean and normalizing to the standard deviation. Then, linear kernel PCA was applied. The number of principal components was the maximum available and was determined by the number of samples in each class. For example, there were seven principal components (PCs) for the U87-3 group. Hereinafter, PC1 is the first principal component, PC2 is the second, etc. The results of the outlier removal and PCA implementation are shown in Figure 8. The data for PC1 and PC4 in the third week of the experiment were the most informative. The change of point positions in the principal component subspace is due to the fact that PCA was applied to a reduced THz spectral matrix after outlier removal. In our previous work we reported positive test results for application of SVM for THz spectral data [16], so we expected good results in this study also. The comparison of the performance of RF, XGBoost, and SVM for THz spectra analysis of glioma is a subject of further research, to be published separately. We excluded artificial neural networks (ANN) from the consideration, because it is difficult to perform important feature selection in such cases: the only working option is the Shapley values method with SHAP algorithm, but this has limitations [42]. Furthermore, for a small dataset, ANN can generate an overfitted model, being too complex with poor data generalization ability. A linear kernel SVM with default parameters was applied to data transformed into the PC feature space. Data model validation was performed by 10-fold CV with averaging and randomly balanced partitioning relative to the size of the original classes, because the number of samples in each class did not exceed 10. The quality of the predictive data model was estimated using the averaged specificity, sensitivity, accuracy (Table 3), and ROC-AUC analysis (Figure 9). Sensitivity is a measure of how well a data model describes true positive cases (i.e., tumor predicted as tumor), while specificity is a similar measure for true negative cases (i.e., non-tumor predicted as non-tumor). Accuracy describes a combination of random and systematic observational error: high accuracy means both high precision and high trueness [43]. It should be noted that, in the case of highly imbalanced class sizes, measurement of classifier performance by balanced accuracy and Matthew's correlation coefficient is recommended [44]. In our case, the size of each class was the same, so we opted to use sensitivity, specificity, accuracy, and ROC-AUC metrics. The extracted informative principal components were derived from the proximity criteria of the reference vector in the SVM to the separating hyperplane. As mentioned, after determining the informative principal components by analyzing the load matrix, informative frequencies were found.