## 3 Results  
A presentation of the CMI groups in a feature space using t-SNE and PCA is shown in Figure 6. According to the t-SNE data presentation (Figure 6a), CMI group 1 (except six red dots near the region with coordinates (\(-2\), \(-2\)) corresponding to the spectra of one sample) is separated from CMI groups 2 and 3. The points from CMI groups 2 and 3 are widely spread and mixed between each other. This is owing to the side effects of the injections still being in place. This result is consistent with the conclusions based on a \({}^{1}\)H-MRS analysis that neuro inflammation disappears by the third week [64]. According to the PCA data presentation (Figure 6b), the CMI groups separation is worse compared to that of t-SNE. Additional PCA projections for the CMI groups are shown Figure S1, Supplementary Materials, which confirms that there is no separability between the groups for the additional principal component projections. A pair-wise comparison of the CMI groups (the first vs. the second weeks, the first vs. the third weeks, and the second vs. the third weeks) in terms of quality metrics and informative features was conducted. The best ROC-AUC metrics were achieved by the SVM and Catboost classifiers (see Figure 7). Full ROC-AUC graphs for all classifiers and all CMI groups are presented in Figure S2, Supplementary Materials. All classifiers demonstrated very good performance metrics (see Table 3). The ideal separability was between CMI groups 1 and 3, which confirms previous conclusions about the neuro inflammation period. CMI groups 2 and 3 are not distinguished very accurately (see Figure S2d,f), so the extraction of informative features differentiating them can be misleading. Figure 6: t-SNE (**a**) and PCA (**b**) visualization of the CMI groups. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Classifier** & **CMI Group 1 vs. 2** & **CMI Group 1 vs. 3** & **CMI Group 2 vs. 3** \\ \hline SVM & 0.99 & 0.99 & 0.74 \\ RF & 0.98 & 0.99 & 0.88 \\ Catboost & 0.98 & 0.99 & 0.92 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mean ROC-AUC metrics of the CMI groups for different classifiers. Figure 7: ROC-AUC analysis of CMI groups: 1 st vs. 2 nd weeks using SVM (**a**), 1 st vs. 3 rd weeks using Catboost (**b**), and 2 nd vs. 3 rd weeks using Catboost (**c**). The results of the informative feature extraction by Catboost and SVM allowing the pair-wise classification of CMI group 1 versus CMI group 2 and CMI group 1 versus CMI group 3 are shown in Figure 8. A detailed analysis of the informative features for all groups and classifiers is presented in Figure S3, Supplementary Materials. The results of the SVM application coincide, but those of the Catboost application are different. The latter is explained due to the computation of informative features in the extreme gradient boosting methods. The more weight a feature has, the more often it is used to separate data in each tree. Thus, a simple voting scheme was used for verifying the informative features discovered by different classifiers, and the following spectral features: 0.35, 0.45, 0.55, 0.7, 0.9, and 1.05 THz were selected. These frequencies are potential TBI markers. CMI group 1 and the GBM group 3 were compared to differentiate TBI and GBM (see Table 4). All classifiers are equally good in terms of AUC metrics, however, the specificity value for SVM and RF has a high variance. According to Figure 9, the informative features distinguishing TBI and GBM via SVM are 0.37, 0.40, 0.55, 0.60, 0.70, and 0.90 THz. The results were the same for RF and Catboost (see Figure S4, Supplementary Materials).