## 3 Results and Discussion
### Data Analysis  
After binning, centering, and unit-variance scaling applications, the OPLS-DA analysis took place for the dataset of spectroscopic measurements. The number of components used was four, with one predictive component and four orthogonal components. Regarding  
Figure 2: Representative samples of Kefalotyri cheese database regarding species’ origin: (**1**) 2924 cm\({}^{-1}\), (**2**) 1746 cm\({}^{-1}\), (**3**) 1634 cm\({}^{-1}\), (**4**) 1460 cm\({}^{-1}\), and (**5**) 1163 cm\({}^{-1}\). \({}^{1}\)H-NMR, all of the data obtained were found to be necessary for the extracted model; however, the most important region from the FTIR spectra was 1900-400 cm\({}^{-1}\), as in our previous studies ([PERSON] and [PERSON] [6] and [PERSON] et al. [5]). As can be seen from Figure 3, only two groups were obtained--(1) cow-origin and (2) goat-and-sheep-origin samples--as was initially expected. Even though most of the samples were semi-hard and hard cheese types, there were no outliers in the model. The outcomes presented in Figure 3 and Table 2 are satisfactory, as samples from cow origin are clearly positioned on the left side of the graph, while samples from goat and sheep origins are consistently shown on the right side. In addition, 100% correct classification was obtained for the two classes regarding the species origin. It must be mentioned that it still remains a great challenge to discriminate goat and sheep samples when both categories fall in the same group, as has also happened in previous studies [5; 6]. Figure 3: (**a**) Score scatter plot (to1/t1) from OPLS-DA modeling, regarding the animal species origin for all the data obtained from the \({}^{1}\)H-NMR spectra and the region 1900-400 cm\({}^{-1}\) from FTIR. A = 1 + 4 components, R2X(cum) = 0.999, R2Y(cum) = 0.970, Q2(cum) = 0.836, and (**b**) 3D presentation (to2/t1/t01) of the score scatter plot in (**a**). Even if 100% correct classification was obtained for the OPLS-DA model, the R2X(cum), R2Y(cum), and Q2(cum) are not equal to 1. R2X(cum) = 0.999 and R2Y(cum) = 0.970 are very close to 1; however, Q2(cum) = 0.836 is a bit lower. The literature has highlighted the challenge of establishing definitive limits for parameters associated with good predictability, as this predictability is heavily influenced by the dataset's characteristics [23; 28]. For instance, determining an acceptable threshold for Q2 depends greatly on the number of observations included. In recent years, several SIMCA PLS-DA or OPLS-DA models have been reported with Q2 values below 0.4, or even below 0.3 [29; 30]. To validate models with seemingly poor predictability, permutation tests are commonly employed. These tests involve comparing the Q2 obtained for the original dataset with the distribution of Q2 values calculated when original Y values are randomly assigned to individuals, as illustrated in Figure 4. Green circles represent R2, while blue squares represent Q2. The values in the top right corner, where correlation = 100%, correspond to the R2 and Q2 values for the actual dataset. The intersection provides an estimate of the overfitting phenomenon. As expected, the initial Y variable demonstrates significantly higher Q2 and R2 values compared to the permuted counterparts. The results of the permutation test indicate that the model effectively accounts for 100% of the overall variance in the data array. ROC curves were generated for the model, and it shows excellent performance with area under the curve (AUC) values for both classes equal to one, as shown in Figure 5. These findings robustly affirm that the observed group separations in the OPLS-DA score scatter plot were statistically significant, and the predictability was not a result of overfitting the data. Subsequently, the extracted OPLS-DA model presented in Figure 3 is considered a good database for future use and predictions of unknown cheese samples while investigating species' origin.