## 3 Results and Discussion
### Classification of EVOOs According to Geographical Origin  
A second classification model was built by using only the Koroneiki samples to discriminate them according to their region of origin (Crete and the Peloponnese). The scores plot of the PLS-DA model is presented in Figure 4.  
It is evident that the samples from the two regions are separated satisfactorily in the two first factors, although there is a partial overlap. To overcome this problem, OPLS-DA was performed (Figure 5a). The advantage of OPLS-DA compared to PLS-DA is that the between-class separation is found only in the first predictive component (x-axis), whereas the uncorrelated variation (which represents the within-class variation) is indicated in the orthogonal components [19]. The OPLS-DA model can classify the samples into the correct geographic region. The goodness-of-fit parameters for the OPLS model, R2X, R2Y and Q2Y, were equal to 0.577, 0.889 and 0.745, respectively. R2X and R2Y represent the proportion of the variance of X and Y variables explained by the model, whereas Q2Y indicates the predictive ability of the model. The closeness of R2Y and Q2Y values to one suggests a more stable and reliable model. The significance of class discrimination was verified by performing a permutation test (\(p<0.01;0/100\)) (Figure S4). According to the VIP (variable  
Figure 4: Multivariate analysis of EVOO samples of Koroneiki cultivar from the Peloponnese (PEL) and Crete (CRE). PLS\(-\)DA scores plot (red dots—PEL; blue squares—CRE). The ellipse represents the [PERSON]’s T2 critical limit. in projection) list of S-plot, a total of 28 volatiles with VIP \(>\) 1 were selected as the most contributing variables to class separation (Figure 5b). The nonparametric Kruskal-Wallis rank sum test was also run to confirm their significance (FDR \(<\) 0.05). Subsequently, multivariate ROC curve analysis was performed to reduce the number of important volatile compounds and evaluate the performance of the models. According to the ROC curves plot (Figure S5a) and the predictive accuracies plot (Figure S5b), the models with 5, 10, 20 and 28 volatile compounds have similar AUC (area under the curve) values, ranging from 0.920 to 0.934, and similar predictive accuracies, ranging from 86.5% to 87.8%. Thus, we selected the five-compound model, consisting of ethyl acetate, 2-methoxyphenol, 2-methyl-1-propanol, 4,8-dimethylnona-1,3,7-triene and 3-ethyl-1,5-ocadiene (Figure S5c) for further ROC analysis. Then, two-thirds of samples were selected as a training-cross-validation set, and the remaining samples were used for external validation (hold-out set) purposes. The combination of the five selected volatile compounds could correctly predict the 88.3% of samples in the cross-validation (CV) set with the corresponding AUC equal to 0.955 and could correctly predict the 100% of samples in the hold-out set with the corresponding AUC equal to 1.00 (Figure 6). Thus, the combination of the prospective biomarkers appears to have the potential to distinguish the Koroneiki EVOOs from the two geographic regions studied. However, a larger number of samples is required to confirm this finding. Classification of Greek EVOOs according to geographical origin has also been reported in the literature. [PERSON] et al. [24], using multivariate analysis (LDA), differentiated olive oil samples from Heraklion (Crete) and Etoloakramania from those originating from Lakonia and Messinia (Peloponnese) with an overall classification rate 93.2%. [PERSON] et al. [12] discriminated satisfactorily olive oils from the Ionian Islands (Zakynthos, Kefalonia, Lefkada and Kerkyra) of western Greece. Some of the most discriminant compounds selected for the classification of the samples according to geographical origin, coinciding with those that emerged from the current study: 3-ethyl-1,5-ocadiene and 4,8-dimethyl-1,3,7-nonatriene. Apart from olive oil samples from Greek growing areas, the results occurring from other oil-producing countries are also promising.