# Chemometric Classification of Feta Cheese Authenticity via ATR-FTIR Spectroscopy
## 3 Results
### Classification Models  
Supervised classification using PCA followed by linear discriminant analysis (PCA-LDA) demonstrated strong discriminative power across all preprocessing strategies (Table 2). Model performance improved progressively from raw spectra to first- and second derivative representations. Using raw spectra with 10 principal components, the model achieved a training AUC of 0.849 and a test AUC of 0.916. However, while sensitivity was perfect on the test set, specificity dropped to 0.545, suggesting a tendency to misclassify non-Feta cheseses as Feta. However, derivative preprocessing significantly enhanced model performance. When using the first derivative, the model with nine PCs achieved 100% sensitivity and nearly 82% specificity, with an overall accuracy of almost 92%. Second derivative preprocessing produced the best training performance (AUC = 0.980), with similarly high-test sensitivity and specificity. These results confirm that applying spectral derivatives enhances class-separating features while reducing overfitting risk, indicating that PCA-LDA is a reliable approach for distinguishing Feta from non-Feta white brined cheeses. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Train Set**} & \multicolumn{4}{c}{**Test Set**} \\ \hline
**Preprocessing** & **\# PCs** & **AUC** & **Sensitivity** & **Specificity** & **AUC** & **Sensitivity** & **Specificity** & **Accuracy** \\ \hline
**Raw Spectra** & 10 & 0.849 & 0.913 & 0.693 & 0.916 & 1.000 & 0.545 & 0.792 \\ \hline
**First Derivative** & 9 & 0.948 & 0.970 & 0.793 & 0.951 & 1.000 & 0.818 & 0.917 \\ \hline
**Second Derivative** & 7 & 0.980 & 0.970 & 0.827 & 0.930 & 1.000 & 0.818 & 0.917 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: PCA-LDA classification performance metrics for raw, first derivative, and second derivative FTIR spectra. Figure 2: PCA of FTIR spectra for Feta (\(\bullet\)) and non-Feta white brined cheese (\(\blacktriangle\)) under raw absorbance (**A**,**B**), first derivative (**C**,**D**), and second derivative (**E**,**F**) preprocessing. Score plots (**A**,**C**,**E**) and scree plots (**B**,**D**,**F**) show PC1/PC2 variance explained. Colored dashed lines indicate group separation boundaries: red for Feta, blue for non-Feta white brined cheese. Partial least squares discriminant analysis (PLS-DA) yielded high classification performance across all spectral preprocessing methods, with notable improvements when using derivative spectra (Table 3). The model based on raw spectra (eight latent variables) achieved a high AUC in the training set (0.992), with a sensitivity and specificity of 0.970 and 0.929, respectively. However, performance dropped on the test set, where the AUC was 0.874 and specificity decreased to 0.818, suggesting modest overfitting. First derivative preprocessing resulted in a more compact model (three latent variables) and perfect training performance (AUC = 1.000). On the test set, sensitivity remained at 1.000, though specificity declined to 0.727, indicating improved detection of Feta samples but more frequent misclassification of non-Feta cheeses. Second derivative preprocessing provided the most balanced and robust results. The model, with nine latent variables, showed perfect training classification and sustained strong performance on the test set, with AUC = 0.958, sensitivity = 1.000, specificity = 0.909, and overall accuracy of 95.8%. It should be noted that while the choice of nine latent variables (LVs) was based on minimizing the balanced error rate (BER), a model with only two LVs also performed very well on the training set, showing only marginally lower accuracy. This suggests that similar classification power might be achieved with a simpler model, depending on application needs. These results indicate that second derivative transformation enhances discriminative spectral features and generalization capability in PLS-DA models.