## 3 Results and Discussion
### Multivariate Analysis
#### 3.2.2 Partial Least Square Discriminant Analysis  
Since the discriminative power of a classification model is unknown, it is necessary to analyze it using different pre-processing methods [48]. Table 4 shows the results of the PLS-DA model applied to tropical fruits under the four pre-processing methods studied (all results are in Table 5). The mean centering pre-processing method and the first derivative of the Savitzky-Golay (SG) pre-processing method show the best prediction results, with a precision of 100% in all tropical fruits. On the training data set, the precision for mean centering and the first derivative of the SG pre-processing method was 93.06-100% and 98.68-100%, respectively. With the second and third derivatives of the SG pre-processing method, the precision was 80-100% and 84.44-100% on the prediction and training data sets, respectively. These values are higher than those reported by [PERSON] et al. [10], whose precision was 19.35-100% on the training data for classifying five varieties of Balkan paprika. These results varied because of the pre-processing method applied. Moreover, in the study of meat carcass classification using Raman spectroscopy, [PERSON] et al. [32] found that the best PLS-DA model correctly classified 94% of grass-fed versus grain-fed carcass. According to Table 4, the first derivative of the SG pre-processing method produced the best results in the PLS-DA classification model for the training data set, as it correctly classifies the samples in 98.68-100% of cases (P), the samples belonging to its class in 97.43-100% of cases (SE), and the samples not belonging to its class in 98.66-100% of cases (SP). All indicators for the prediction data set were 100%. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Pre-Processing Method**} & \multirow{2}{*}{**Sweet Fruit**} & \multicolumn{4}{c}{**Training Data Set**} & \multicolumn{4}{c}{**Prediction Data Set**} \\  & & **P \({}^{1}\) (\%)** & **SE \({}^{2}\) (\%)** & **SP \({}^{3}\) (\%)** & **P (\%)** & **SE (\%)** & **SP (\%)** \\ \hline \multirow{3}{*}{**Mean centering**} & Cherimoya & **93.06** & 93.87 & 97.98 & 100.00 & 100.00 & 100.00 \\  & Soursop & 97.02 & 97.95 & 96.97 & 100.00 & 100.00 & 100.00 \\  & Pineapple & **100.00** & 98.00 & **100.00** & 100.00 & 100.00 & 100.00 \\ \hline \multirow{3}{*}{**First derivative of Savitzky-Golay**} & Cherimoya & **100.00** & 97.43 & **100.00** & 100.00 & 100.00 & 100.00 \\  & Soursop & 98.68 & **100.00** & 98.66 & 100.00 & 100.00 & 100.00 \\  & Pineapple & **100.00** & **100.00** & **100.00** & 100.00 & 100.00 & 100.00 \\ \hline \multirow{3}{*}{**Second derivative of Savitzky-Golay**} & Cherimoya & 96.68 & 54.83 & 98.11 & 100.00 & 12.50 & 100.00 \\  & Soursop & 84.44 & 92.00 & 83.05 & 80.00 & 100.00 & 75.00 \\  & Pineapple & **100.00** & 89.28 & **100.00** & 100.00 & 100.00 & 100.00 \\ \hline \multirow{3}{*}{**Third derivative of Savitzky-Golay**} & Cherimoya & 98.13 & 71.79 & 98.61 & 100.00 & 20.00 & 100.00 \\  & Soursop & 87.94 & 97.22 & 86.67 & 80.59 & 69.23 & 83.33 \\ \cline{1-1}  & Pineapple & **98.68** & **100.00** & 98.67 & 100.00 & 100.00 & 100.00 \\ \hline \hline \end{tabular} \({}^{1}\) Precision (P), \({}^{2}\) Sensitivity (SE) or true positive rate, \({}^{3}\) Specificity (SP) or true negative rate.  
\end{table} 
Table 4: Classification results of the PLS-DA model.