## 3 Results and Discussion
### Multivariate Analysis
#### 3.2.1 Principal Component Analysis  
PCA is a chemometric method that allows us to explore patterns [43] and is almost always the first analysis performed on a multivariate data set [44]. The acquired spectral data set may be disturbed by random noise during acquisition; therefore, pre-processing methods are necessary to improve the PCA results. Pre-processing methods can reduce the random noise and improve the spectral characteristics of interest [45]. Figure 3 shows the results of the four pre-processing methods applied to the cherimoya, soursop, and pineapple spectral data sets. The mean centering method (Figure 3a) produced the least visible changes in the corrected spectra compared to the Savitzky-Golay first (Figure 3b), second (Figure 3c) and third (Figure 3d) derivative method. These effects can be observed in the intensities and positions of the peaks. The changes in the model performance indicators are presented to highlight the effect of the pre-processing methods on the model [45]. Table 2 reports the root mean square error for cross-validation (RMSECV), which is an internal validation error estimated according  
Figure 2: Chemometric analysis of raw (**a**) and corrected (**b**) Raman spectra of cherimoya, soursop, and pineapple. to [PERSON] et al. [46]. Table 2 shows that when the SG first derivative pre-processing method was used, the PCA model was composed of four principal components that captured 92.59% of the total data variance and 7.41% of the Q residuals (Table 3). [PERSON] et al. [21] used a plot of [PERSON]'s T2 vs. Q residuals to eliminate four spectra identified as outliers for the discrimination between transgenic and conventional cotton seeds. Figure 4 was obtained after removing two outliers and shows that cherimoya was separated from the other fruits using the four pre-processing methods. However, none became an outlier, since it was at most 95%. The mean centering pre-processing method produced a three-component PCA model with a captured variance of 76.05%, which is the lowest captured variance among the models (Table 2). In the score plot, a better sample separation can be observed due to the formation of three well-defined clusters (Figure 5). Cherimoya and soursop, which belong to the Annonaceae family [47], form clusters closer to each other because they share many Raman peaks (including sugars), such that their chemical compositions are similar, unlike pineapple, which belongs to another family (Bromeliaceae) and has a different chemical composition. The separation of the clusters may be caused by the differences in the fruits' phytochemical compound content, such as polyphenols, vitamins, fiber, and carotenoids. The loading plot of the first principal component produced by the four pre-processing methods (Figure 5) shows more pronounced peaks in the 1000-1200 cm\({}^{-1}\) band, where the characteristic glucose peak (common to the three tropical fruits) is found. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Pre-Processing Method** & **PC** & **RMSECV** & **\% Variance Captured Total** & **Q Residual** & **Hotelling’s T2** \\ \hline Mean centering & 3 & 254.18 & 76.05 & 23.95 & 76.05 \\ First derivative of Savitzky–Golay & 4 & 44.06 & 92.59 & 7.41 & 92.59 \\ Second derivative of Savitzky–Golay & 5 & 25.86 & 91.10 & 8.90 & 91.10 \\ Third derivative of Savitzky–Golay & 5 & 39.32 & 81.06 & 18.94 & 81.06 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Effect of four data pre-processing methods on the PCA model for cherimoya, soursop, and pineapple.