## 3 Results and Discussion
### Valorization of Prickly Pear Juice Geographical Origin Based on Mineral Content Using LDA
Application of PCA and LDA in the mineral content of lemon juice samples resulted in their correct classification according to geographical origin by 93.2%; higher by 7.5% compared to present results. Valorization of Prelky Pear Juice Geographical Origin Based on Semi-Quantitative Data of Volatile Compounds Using LDA  
Similarly, [PERSON]'s trace = 1.932 (F = 11.444, df = 50, \(p<0.001\)) and [PERSON] lambda = 0.000 (F = 16.335, df = 50, \(p<0.001\)) index values showed that there was a significant multivariable effect of volatile compounds on geographical origin of prelky pear juice. Twenty-two volatile compounds were found to be significant (\(p<0.05\)) for the geographical discrimination of prelky pear juice samples. To avoid any misleading source, it should be stressed that 2-pentyl-furan, despite the significant differences (\(p<0.05\)) among prelky pear juice samples according to geographical origin, was not included in the  
Figure 2: **(a)** Classification of prelky pear juice according to geographical origin based on 7 minerals and linear discriminant analysis (LDA). **(b)** Classification of prelky pear juice according to geographical origin based on 21 volatile compounds and LDA. statistical analysis because it was categorized as a thermal artifact. Therefore, the semi-quantitative data of 21 volatile compounds was subjected to LDA. Two canonical significant discriminant functions, as in the case of minerals, were formed: Wilks' Lambda = 0.001, \(X^{2}\) = 159.643, df = 42, \(p\) < 0.001 for the first and Wilks' Lambda = 0.103, \(X^{2}\) = 52.338, df = 20, \(p\) < 0.001 for the second function, respectively. The first discriminant function recorded the higher eigenvalue (105.215) and canonical correlation of 0.995, accounting for 92.3% of total variance. The second discriminant function recorded a much lower eigenvalue (8.733) and canonical correlation of 0.947, accounting for 7.7% of total variance. Both accounted for 100% of total variance which is a perfect rate. As it may be seen in Figure 2b, prickly pear fruit juices are clearly separated. The correct classification rate was 100% using the original and 88.9% using the cross-validation method. The geographical classification rate was 75%, 91.7%, and 100% for Western Messinia, Eastern Messinia and Lakonia, respectively (Table S11). Respective group centroid values were: (-3.469, -3.875), (-9.912, 2.803), and (13.381, 1.072) for Western Messinia, Eastern Messinia and Lakonia regions. The volatile compounds which served as markers of prickly pear juice geographical origin are listed in Table 4. However, differences in the volatile profile and as a consequence, in the classification rates obtained, may also be attributed to genetic factors (i.e., cultivar) [32; 33], given the fact that wild-grown prickly pear cultivars from specific regions were used in the study. In a relevant study, [PERSON] et al. [10] used SPME-GC/MS for the determination of volatile compounds in apple juice prepared from different varieties. Further application of LDA in the volatile compounds data, resulted in the correct classification rate of apple juice samples by 87.5%. More recently, application of SPME-GC/MS and principal component analysis on the volatile compounds identified in tomato juice from Italian and Spanish markets resulted in the explanation of 68.61% of total variance among the samples analyzed [43].