## 2 Results and Discussion
### Classification of Cretan VOO Samples  
EVOO flavor is considered a significant quality but may also be utilized as a classification criterion. VOO volatile profile plays a fundamental role in defining the geographical origin of oils. The majority (roughly 70%) of PDO/PGI olive oils in Greece are produced in the Peloponnese and Crete. Six of the ten Cretan PDOs come exclusively from Koroneiki, the main Greek cultivar and also the most prominent in Crete; three include blends of 90% Koroneiki VOO, and only one contains blends of 60% oil from Tsounati, the second most significant Cretan cultivar [41]. One PDO was registered for the entire Lasithi regional unit, whilst two PDOs from Chania come from two distinct terroirs but include comparable blends of Koroneiki and Tsounati oils. It is essential that these specific PDOs be subjected to thorough administrative control. These objective criteria, including organoleptic ones, should be accessible to support the authenticity and prevent attempts at fraud. In the current study, the potential of the newly developed method was investigated for its use in the classification of Cretan VOO samples with the aid of multivariate statistical analysis. The obtained data were analysed using multivariate statistical analysis models to identify correlations between VOC profiles and VOO geographical origin; thus, chromatographic peak areas were used for modelling the differences between the studied groups. The overall performance of the analytical method was evaluated by assessing the variability of the detected compound in QC samples. All the compounds in QC samples presented % RSD < 30%, indicating satisfactory stability and reproducibility of the analytical system during the analytical batch. As shown in Figure S2, principal component analysis (PCA) was used to evaluate the analytical system's suitability and reproducibility (QC cluster). Group differentiation and identification of potential markers related to geographical origin were performed by latent structures OPLS DA analysis. Before the assessment of geographical origin to the volatile fingerprint of VOOs, the effect of farming type (organic vs. conventional) was examined. Multivariate statistical analysis was performed to samples from each area produced with different cultivation types. It was observed that farming type is not a statistically significant factor for the specific samples, and thus geographical origin assessment was further performed using both sample types (organic and conventional). Initially, VOO samples from nearby production regions such as Chania-Rethymnon, Rethymnon-Heraklion and Lasithi-Heraklion (Figure S3) did not present any statistically significant differences regarding their volatile content. Although the region of Chania is located on the western side of Crete and Heraklion roughly in the middle of the island, the content of VOOs was not affected by the different origins due probably to other stronger common factors that may affect the VOO profile, which may include climate, fruit maturity, and processing technology [5]. The impact of geographical origin was found significant when VOOs from Lasithi, the easternmost region of Crete, were compared with samples from Chania and Rethymnon. The respective orthogonal projection to latent structures discriminant analysis (OPLS-DA) models are illustrated in Figure 5a,b, where samples with the same origin are clustered together and show clear differentiation against samples from Lasithi. Clear separation was observed between VOOs from Chania and Lasithi and between VOOs from Lasithi and Rethymnon with cross-validated ANOVA analysis (CV Analysis), \(p\) = 0.0008 and \(p\) = 0.02, respectively. Permutation tests showed that the models were robust, with high predictability (R2Y (cum) and Q2 values of 0.827 and 0.656 and 0.881 and 0.453, respectively). Studying the multivariate loadings vectors in each case revealed various analytes related to the differentiation between the studied groups.