## 3 Results and Discussion
### Valorization of Prickly Pear Juice Geographical Origin Based on Mineral Content Using LDA  
MANOVA analysis identified the significant minerals that could be used for the geographical discrimination of prickly pear juice samples. The sixteen minerals were considered as the dependent variables, while the three regional zones (geographical origin) were taken as the independent variables. The two qualitative criteria of multivariate statistics namely [PERSON]'s trace = 1.694 (F = 6.571, df = 32, \(p\) < 0.001) and [PERSON] lambda = 0.022 (F = 6.469, df = 32, \(p\) < 0.001), showed that there was a statistically significant effect of prickly pear juice mineral content on the geographical origin of fruit juices. In particular, 7 of the 16 minerals (Table 3) were found to be significant (\(p\) < 0.05) for the geographical discrimination of prickly pear juices. These minerals were, then, subjected to LDA. In addition, the minimum tolerance level of the analysis was set at 0.001. Results showed that Fe did not pass the tolerance test. Therefore, it was excluded (SPSS program) a priori from the discriminant analysis. During LDA analysis two canonical discriminant functions were formed: Wilks' lambda = 0.063, X\({}^{2}\) = 80.320, df = 14, \(p\) < 0.001 for the first function and Wilks' lambda = 0.348, X\({}^{2}\) = 30.611, df = 6, \(p\) < 0.001, for the second. The first discriminant function recorded the higher eigenvalue (4.552) and canonical correlation of 0.905, accounting for 70.8% of total variance. The second discriminant function recorded a lower eigenvalue (1.874) and canonical correlation of 0.807, accounting for 29.2% of total variance. Both accounted for 100% of total variance. Prickly pear fruit juices are well separated, as shown in Figure 2a. The classification rate was 94.3% using the original, and 85.7% using the cross-validation method. The geographical classification rate was 91.7%, 81.8%, and 83.3% for Western Messinia, Eastern Messinia, and Lakonia, respectively (Table S10). The group centroid values, characteristic for each geographical origin, are also pointed out in Figure 2a. What should be defined, is that each centroid has two numbers which represent the coordinates. The abscissa is the first discriminant function and the ordinate is the second. The respective group centroid values were: (\(-\)1.899, 1.341), (\(-\)0.954, \(-\)1.834), and (2.774, 0.340) for the Western Messinia, Eastern Messinia, and Lakonia regions. The farther apart the means are, the less error there will be in classification [17]. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Minerals** & **Wilks’ Lambda** & **F** & **df1** & **df2** & \(p\) & **Function 1** & **Function 2** \\ \hline Ca & 0.748 & 5.397 & 2 & 32 & 0.0010 & 0.132 & 0.371 * \\ K & 0.458 & 18.938 & 2 & 32 & \(<\)0.001 & 0.463 * & \(-\)0.334 \\ Mg & 0.797 & 4.070 & 2 & 32 & 0.027 & 0.230 * & \(-\)0.086 \\ Na & 0.770 & 4.768 & 2 & 32 & 0.015 & 0.025 & \(-\)0.397 * \\ Ni & 0.746 & 5.439 & 2 & 32 & 0.009 & \(-\)0.047 & \(-\)0.419 * \\ P & 0.428 & 21.397 & 2 & 32 & \(<\)0.001 & 0.381 & \(-\)0.600 * \\ Zn & 0.704 & 6.741 & 2 & 32 & 0.004 & 0.081 & 0.457 * \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Contribution of minerals to the canonical discriminant function structure matrix. [PERSON] et al. [9] used inductively coupled plasma atomic emission spectroscopy (ICP-AES) and inductively coupled plasma mass spectrometry for the determination of minerals and trace elements (Al, B, Ba, Ca, Co, Cu, Fe, K, Li, Lu, Mg, Mn, Mo, Na, Ni, P, Rb, Si, Sr, Sn, Ti, V, and Zn) in Australian and Brazilian orange juice samples. Principal component analysis (PCA) in mineral and trace element contents resulted in a clear differentiation of orange juice samples. In another study, [PERSON] et al. [13] used instrumental neutronic activation analysis (INAA) for the determination of Br, As, Na, Rb, La, Cr, Sc, Fe, Co, Zn, and Sb in lemon juice samples collected from three different geographical origins in the northwest region of Argentina.