## 3 Results and Discussion
### Stepwise-LDA of Fluorescence Spectra  
The chemometric analysis of fluorescence spectra (\(\lambda\)ex = 330 and 360 nm) for the classification of thyme, pine, fir, and citrus honey was performed using the stepwise-LDA algorithm. After random separation of the samples, the ratio of the largest group (thyme honey) divided by the smallest group (citrus honey) was calculated at 1.5, confirming the homogeneity of the covariance matrices. Subsequently, the calibration set (\(n\) = 59) was subjected to a stepwise algorithm under the Mahalanobis distance method. Following the development of LDA models, their performance was evaluated using the cross-validation method. Furthermore, a test set (\(n\) = 28) was used for external validation to examine the robustness of the models. The chemometric model, based on \(\lambda\)ex = 330 nm, demonstrated that nine stepwise steps (\(p\) < 0.05) were formed. The score values for both calibration and cross-validation were 94.9%. The group centroid values are also plotted in Figure 8.  
The results of the Wilks's lambda (\(\Lambda\)) of the canonical functions (first: 0.120, \(p\) < 0.05; second: 0.240, \(p\) < 0.05; third: 0.653, \(p\) < 0.05) indicated a significant difference between the mean vectors of the four honey botanical origins. Additionally, the eigenvalues and canonical correlation of the discriminant functions (first: 18.213, 97.4%; second: 1.724, 79.6%; third: 0.531, 58.9%) confirmed the calibration model. After, external validation of \"unknown\" samples evaluated the ability of the discrimination. A total of 82.1% were correctly classified while 17.9% were misclassified. Hence, a low variation between the  
Figure 8: Discrimination results based on \(\lambda\)ex = 330 nm. cross-validation and external validation indicates good performance of the chemometric model to predict new data (Table 3). When applying the stepwise algorithm on \(\lambda\)ex = 360 nm spectra three steps were formed (\(p\) < 0.05). The separation of the four honey botanical origins are shown in Figure 9. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & & \multicolumn{4}{c}{**Predicted Group Membership**} \\ \cline{3-8}  & **Labels** & \
\begin{tabular}{c} **Thyme** \\ **Honey** \\ \end{tabular} & **Pine Honey** & **Fir Honey** &
\begin{tabular}{c} **Citrus** \\ **Honey** \\ \end{tabular} & **Total** \\ \hline \multirow{6}{*}{Original a  \\ \cline{2-8}  & \multirow{2}{*}{\%} & Thyme honey & 18 & 0 & 0 & 0 & 18 \\ \cline{3-8}  & & Pine honey & 1 & 11 & 1 & 0 & 13 \\ \cline{3-8}  & & Fir honey & 0 & 1 & 15 & 0 & 16 \\ \cline{3-8}  & & Citrus honey & 0 & 0 & 0 & 12 & 12 \\ \cline{3-8}  & & Thyme honey & 100.0 & 0.0 & 0.0 & 0.0 & 100.0 \\ \cline{3-8}  & \multirow{2}{*}{\%} & Pine honey & 7.7 & 84.6 & 7.7 & 0.0 & 100.0 \\ \cline{3-8}  & & Fir honey & 0.0 & 6.3 & 93.8 & 0.0 & 100.0 \\ \cline{3-8}  & & Citrus honey & 0.0 & 0.0 & 0.0 & 100.0 \\ \hline \multirow{6}{*}{Cross-validated b,c  \\ \cline{3-8}  & \multirow{2}{*}{Count} & Thyme honey & 100.0 & 0.0 & 0.0 & 0.0 & 100.0 \\ \cline{3-8}  & & Pine honey & 7.7 & 84.6 & 7.7 & 0.0 & 100.0 \\ \cline{3-8}  & & Fir honey & 0.0 & 6.3 & 93.8 & 0.0 & 100.0 \\ \cline{3-8}  & & Citrus honey & 0.0 & 0.0 & 0.0 & 100.0 & 100.0 \\ \hline \multirow{6}{*}{External Validation d  \\ \cline{3-8}  & \multirow{2}{*}{Count} & Thyme honey & 11 & 0 & 3 & 0 & 14 \\ \cline{3-8}  & & Pine honey & 1 & 4 & 0 & 0 & 5 \\ \cline{3-8}  & & Fir honey & 0 & 1 & 4 & 0 & 5 \\ \cline{3-8}  & & Citrus honey & 0 & 0 & 0 & 4 & 4 \\ \cline{3-8}  & & Thyme honey & 78.6 & 0.0 & 21.4 & 0 & 100.0 \\ \cline{3-8}  & & Pine honey & 20.0 & 80.0 & 0.0 & 0 & 100.0 \\ \cline{3-8}  & & Fir honey & 0.0 & 20.0 & 80.0 & 0 & 100.0 \\ \cline{3-8}  & & Citrus honey & 0.0 & 0.0 & 0.0 & 100.0 & 100.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Discrimination results based on fluorescence at \(\lambda\)ex = 330 nm. Group centroids of pine and fir honey failed to display the same clear separation as was evident between the thyme and citrus honey.