## 3 Results and Discussion
### Pattern Recognition Analysis  
All sample spectra were normalized using VN preprocessing. Then, they were evaluated using Pre-CLS. The soil database used for the evaluation initially contained QCL reflectance spectra of four different natural soils, sand, and clay standards. It was expanded using linear combinations of sand and clay by applying the concept of Self-Simulated Learning Artificial Intelligence (SSLAI). SSLAI consists of an Artificial Intelligence method that uses minimal information to develop the Machine Learning models. In this case, other types of soils are simulated using those that are available, and these new simulated soils are used for the analysis. FSA algorithm for Pre-CLS was applied for spectra of the samples, and one spectrum of the database was added to the model (see Equation (7)) for most spectra. Next, the sum of \(\beta_{j}\) (SUM(\(\beta\))) parameters was calculated without including the bias (\(\beta_{0}\)), and a simple binary discrimination model was generated and evaluated (see Table 6) using this parameter to distinguish between contaminated and clean soils. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Precision** & **Recall** & **F1-Score** & **Support** & **Accuracy** & **Matrix of Confusion** \\ \cline{2-7}  & & & Model & & EXP & NONE \\ \hline EXP & 0.768 & 1.000 & 0.869 & 1126 & 0.877 & 865 & 261 \\ NONE & 1.000 & 0.793 & 0.884 & 997 & 0 & 997 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Confusion matrix and evaluation criteria for the binary discrimination model using SUM (\(\beta\)) parameters. Figure 5: Dependence of the root-mean-square error of cross-validation (RMSECV) on LV for the considered interferences: the NAT-S optimization of the validation set (OPT-Val) and NAT-S models. Figure 6a shows the probability distribution of SUM (\(\beta\)) for the two classes of the binary model. In this figure was observed a broad distribution of SUM (\(\beta\)) for the samples contaminated by explosives (EXP), it is due to the range of concentrations. Additionally, when samples EXP has the highest concentration of HEs, the value SUM (\(\beta\)) approaches 0 because it has the lowest proportion of soil. On the other hand, in the NONE sample, the distribution is sharpest, and the SUM (\(\beta\)) is highest. The evaluation criteria (precision, recall, f1-score, and accuracy) and the confusion matrix for the model are shown in Table 6. This model has high precision in predicting clean soils (NONE), whereas it is moderate in predicting contaminated soils (EXP). This is because soils with low explosive concentrations are predicted as clean, increasing the number of false negatives. This happens at low concentrations (<2%), where the model does not work well. Following the scheme illustrated in Figure 1, PCA was applied to the normalized data providing 20 principal components accounting for 99.99% of the variance. These components were normalized using an auto-scale preprocessing, and the SUM (\(\beta\)) was added as an additional principal component. Then, various ML methods were used to generate multi-classification models to discriminate between soils contaminated with three types of explosives (DNT, TNT, and RDX) and clean soil (NONE). These models were evaluated using accuracy and log-loss calculated over the test data (Figure 6b). The best method was RFC. This method constructs a multitude of decision trees during the training process and outputs the class that is the mode of the classes of the individual trees. The evaluation criteria (precision, recall, f1-score, and accuracy) and the confusion matrix calculated for the RFC model over the test data are listed in Table 7. The test data were classified almost entirely. Other strategies such as the generation of models without SUM (\(\beta\)) were also evaluated (data not shown); however, these provided poor results with a high number of false positives, i.e., many samples of clean soil were classified as containing explosives. This was resolved by adding the SUM (\(\beta\)) parameter.