## 3 Results and Discussion
### THz Data Analysis
\begin{table}
\begin{tabular}{c c c c} \hline
**Group Name** & **Number of Outliers** & **Total Count of Samples** & **Outlier Percentage** \\ \hline U87-1 & 1 & 5 & 20\% \\ \hline U87-2 & 1 & 10 & 10\% \\ \hline U87-3 & 2 & 7 & 28\% \\ \hline \end{tabular}
\end{table} 
Table 2: Results of IF application for the initial THz dataset. Figure 8: Results of PCA analysis of THz spectra for (**a**) the first, (**b**) second, and (**c**) third weeks of the experiment, (**left**) without and (**right**) with outlier removal. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Week** & **Outliers Removed** & **Sensitivity** & **Specificity** & **Accuracy** \\ \hline
1 & No & 0.43 & 0.69 & 0.57 \\ \hline
1 & Yes & 1 & 1 & 1 \\ \hline
2 & No & 0.43 & 0.57 & 0.50 \\ \hline
2 & Yes & 0.65 & 0.83 & 0.76 \\ \hline
3 & No & 0.7 & 0.88 & 0.82 \\ \hline
3 & Yes & 0.85 & 1 & 0.93 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Average performance of the SVM classifiers of control vs tumor groups for the first, second, and third weeks of the experiment, with and without outlier removal. It can be seen from Figure 9 that, according to SVM classifiers, the most informative principal component for the first week was PC1, those for the second week were PC4 and PC7, and for the third week PC4 and PC1. It should be mentioned that the SVM accuracy and ROC-AUC values were low for the second week, so those particular informative principal components should not be trusted. With the informative principal components identified using linear SVM, the next step was to analyze the loadings matrix (see Figure 10). The discontinuous cutoff lines in Figure 10 indicate the threshold values: peaks above the positive cutoff line and below the negative cutoff line are considered informative. Figure 9: ROC-AUC analysis and informative principal components chosen by SVM for (**a**) the first, (**b**) the second, and (**c**) the third weeks of the experiment, respectively. Figure 10: PCA loadings matrix analysis for informative feature selection, based on THz data: (**a**) first week, (**b**) second week, and (**c**) third week of the experiment. As shown in Figure 9, the informative frequencies for the first week were 0.11, 0.22, 1.2, 1.6 THz for PC1. For the second week, the informative frequencies were 0.18, 0.35, 1.1, 1.65 THz for PC4. For the third week, the informative frequencies were 0.56, 1.0 THz for PC1, and 0.22, 1.2, 1.48, 1.52, 1.82 THz for PC4. It should be noted that the predictive data model for the second week of the experiment was of inferior quality, so the informative frequencies in that particular case cannot be considered reliable. According to the sample size, we applied Mann-Whitney U testing (\(p\)-value threshold \(>\)0.5, the larger the better) for the selected informative features for the first and the third weeks of the experiment. The results reflected the known problem of using \(p\) value for informative feature selection in high dimensional cases [45,46]; for example, 0.08 THz was found informative, \(p\)-value = 0.81, but ML methods discarded it. It can be seen from the THz spectra plots that the peak at 0.08 THz had large overlapping variance and cannot be considered important. Vice versa, meanwhile, the peak at 0.56 THz had a larger difference in mean and low STD values, but a low \(p\)-value = 0.01. For this reason we do not apply statistics-based informative feature selection in this paper. Study of Relationship between Tumor Size and THz Spectral Profile of Blood Serum by LASSO Regression Method  
The parameter of regularization \(\alpha\) in the LASSO method is critically important, the accuracy of the model depends on the quality of its choice.