## 3 Results
### PLS-DA Analysis  
As mentioned above, four different PLS-DA models were calculated on the training samples, one per each tested pre-treatment. Cross-validated classification rates, together with the number of latent variables (LVs) used for the creation of the models, are reported in Table 1.  
Figure 1: NIR spectra (**a**) raw spectra of all the investigated samples, (**b**) mean spectra of authentic (red line) and adulterated samples (blue line). Inspecting the outcome of the PLS-DA analysis, the first derivative was considered the most suitable preprocessing approach for this data, because the model built on data pretreated by this preprocessing led to the most accurate predictions. The application of this model to the test set led to a correct classification rate of 63.3%, corresponding to 10 authentic and 12 adulterated samples erroneously assigned. It has to be noted that, among the 12 misclassified adulterated samples, 10 are those with the lowest extent of adulteration (5%). Consequently, the counterfeited samples with 5% adulteration were removed from the analysis and new PLS-DA models were calculated on the remaining samples. In this way, the training set consisted of 96 objects (49 authentic and 47 adulterated), and the test set of 40 individuals (23 authentic and 17 adulterated). Data were preprocessed as described before, and PLS-DA models were built and cross-validated; the corresponding results are reported in Table 2.  
In this case the best calibration model was the one built on data preprocessed by SNV. Its application to the test set led to the correct classification of 82.6% of the authentic samples, and 82.4% of the adulterated objects, corresponding to four (over 23) and three (over 17) misclassified samples, respectively. Eventually, in order to investigate which spectral variables most influenced the PLS-DA model, the values of the variable importance in projection (VIP) [53] for the individual predictors were inspected, and 82 NIR wavelengths were identified as significantly contributing (based on the greater than one criterion). A graphical representation of the selected bands is reported in Figure 2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Preprocessing**} & \multirow{2}{*}{**LVs**} & \multicolumn{3}{c}{**\% Correct Classification Rate in Cross-Validation**} \\  & & **Authentic** & **Adulterated 5\% + 10\%** & **Overall** \\  & & **(49 Samples)** & **(91 Samples)** & **(140 Samples)** \\ \hline MC & 5 & 67.3 & 73.6 & 70.4 \\ SNV (+MC) & 4 & 65.3 & 75.8 & 70.5 \\
1 st derivative (+MC) & 6 & 73.4 & 91.5 & 82.4 \\
2 nd derivative (+MC) & 4 & 71.4 & 76.6 & 74.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Partial least squares discriminant analysis (PLS-DA) classification of authentic vs. 5% + 10% adulterated samples: results of cross-validation for model selection. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Preprocessing**} & \multirow{2}{*}{**LVs**} & \multicolumn{3}{c}{**\% Correct Classification Rate in Cross-Validation**} \\  & & **Authentic** & **Adulterated 10\%** & **Overall** \\  & & **(49 Samples)** & **(47 Samples)** & **(96 Samples)** \\ \hline MC & 7 & 67.3 & 83.0 & 75.1 \\ SNV (+MC) & 8 & 83.7 & 91.5 & 87.6 \\
1 st derivative (+MC) & 6 & 73.5 & 91.5 & 82.5 \\
2 nd derivative (+MC) & 5 & 73.5 & 78.7 & 79.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: PLS-DA classification of authentic vs. 10% adulterated samples: results of cross-validation for model selection. In the plot, variables with a VIP higher than one are highlighted in red, over the mean spectrum of the samples (in black). It can be seen that the spectral ranges contributing the most to the discrimination are those between 1040 and 1070 nm, corresponding to the second overtones of N-H stretching, and O-H stretching; those between 950 to 1000 nm, also corresponding to the second overtone of N-H stretching and of O-H stretching; and some variables between 900 and 950 nm, corresponding to the third overtone of C-H stretching [58; 59].