## 3 Results and Discussion
### SVM Analysis  
Unlike the PLS-DA models generated, the SVM model was developed using the full reflectance spectral region (e.g., from 1000 to 1600 cm\({}^{-1}\)) with all soil types, including sea sand with and without petroleum. The classification model used petroleum concentrations ranging from 0% to 12% _w/w_ in all soil samples. Additionally, a second model combining PCA and SVM was introduced. The PCA-SVM model was carried out to establish an SVM model with reduced data dimensions, and six PCs were used. An external evaluation of the classifications for the PCA-SVM and SVM models was almost perfect and is shown in Table 3. The PCA-SVM model has a recall value of samples with petroleum (sensitivity) and recalls value for samples without oil (specificity) of 0.93 for both cases. However, the SVM model generated using all data provided improved results with recall values (sensitivity and specificity) of 1.00 and 0.99, respectively. Table 3 shows the accuracies of the evaluation methods performed on the test sets, and the table data show that the SVM model achieves better accuracy rates when compared with the PCA-SVM model. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{6}{c}{**Soil**} \\ \hline \multicolumn{2}{c}{**\% of P**} & \multicolumn{2}{c}{**Sensitivity**} & \multicolumn{4}{c}{**Specificity**} & \multicolumn{2}{c}{**ROC Area**} \\ \hline  & Cal & CV & Pred & Cal & CV & Pred & \\
0.2 & 0.91 & 0.91 & 0.89 & 0.97 & 0.97 & 0.95 & 0.98 \\
1 & 0.99 & 0.99 & 0.98 & 0.97 & 0.97 & 0.96 & 1.00 \\
5 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\
10 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ \hline \multicolumn{6}{c}{**Sand**} \\ \hline
0.068 & 0.85 & 0.82 & 0.77 & 0.87 & 0.85 & 0.80 & 0.89 \\
0.125 & 0.96 & 0.88 & 0.84 & 0.92 & 0.96 & 0.91 & 0.94 \\
0.25 & 0.99 & 0.98 & 0.94 & 1.00 & 0.97 & 0.93 & 0.99 \\
0.5 & 0.99 & 0.97 & 0.94 & 0.97 & 0.97 & 0.94 & 0.98 \\
1 & 0.99 & 1.00 & 0.98 & 1.00 & 0.97 & 0.95 & 1.00 \\
2 & 0.99 & 1.00 & 0.99 & 1.00 & 0.99 & 0.98 & 0.99 \\
4 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\
8 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ \hline \multicolumn{6}{c}{**All data**} \\ \hline Model-All & 0.93 & 0.92 & 0.91 & 0.93 & 0.92 & 0.88 & 0.94 \\ Model-OPT & 0.96 & 0.96 & 0.94 & 0.96 & 0.96 & 1.00 & 0.99 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Sensitivity, specificity, and receiver-operator curves (ROC) area for each PLS-DA model. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Sample** & **Parameter** & **a** & **b** & **R** & **\
\begin{tabular}{c} **\% for** \\ **p = 93\%** \\ \end{tabular} &
\begin{tabular}{c} **\% for** \\ **p = 50\%** \\ \end{tabular} \\ \hline \multirow{3}{*}{Soil} & Sensitivity (CV) & 0.996 \(\pm\) 0.001 & 0.0205 \(\pm\) 0.0004 & 0.9996 & 0.25 & 0.02 \\  & Specificity (CV) & 1.007 \(\pm\) 0.009 & 0.006 \(\pm\) 0.004 & 0.8477 & 0.08 & 0.006 \\  & ROC Area & 0.9996 \(\pm\) 0.0001 & 0.00332 \(\pm\) 0.00005 & 0.9998 & 0.04 & 0.003 \\ \hline \multirow{3}{*}{Sand} & Sensitivity (CV) & 0.990 \(\pm\) 0.008 & 0.016 \(\pm\) 0.001 & 0.9808 & 0.2 & 0.02 \\  & Specificity (CV) & 1.00 \(\pm\) 0.01 & 0.010 \(\pm\) 0.002 & 0.9336 & 0.1 & 0.01 \\ \cline{1-1}  & ROC Area & 0.995 \(\pm\) 0.005 & 0.0082 \(\pm\) 0.0008 & 0.9576 & 0.1 & 0.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: PLS-DA parameters for the fits for 93% and 50% probabilities for petroleum sensing. The LD and LOD were calculated from the ROC chart (see Figure 6a) using the best model developed by the SVM, and the results are summarized in Table 4. The behavior of the probability of sensing the contaminant using SVM was evaluated by using the equation 4 fitting values of the LOD and LD, which were 0.2% and 0.01%, respectively. These values are below those found in restored soils (2%). To analyze the trade-off between accurate detections and false alarms in the QCL/SVM model, a ROC plot was generated (Figure 6a).