## 3 Results and Discussion
### Single- and Multi-Block Varietal Classification
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Data Block**} & \multirow{2}{*}{**P Pretreatment**} & \multirow{2}{*}{**LVs**} & \multicolumn{2}{c}{**Average Classification Error Rate (CV)**} \\ \hline \multirow{3}{*}{UHPLC} & **Mean-Centering (MC)** & **5** & **0.41** \\  & AutoScaling & 2 & 0.42 \\  & PQN (+MC) & 8 & 0.43 \\ \hline \multirow{3}{*}{ICP-OES} & Mean-Centering (MC) & 5 & 0.34 \\  & AutoScaling & 4 & 0.31 \\  & PQN (+MC) & 8 & 0.29 \\  & **Log10** & **7** & **0.28** \\ \hline \multirow{3}{*}{GC} & **Mean-Centering (MC)** & **6** & **0.43** \\  & AutoScaling & 1 & 0.49 \\ \cline{1-1}  & PQN (+MC) & 5 & 0.48 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: PLS-DA models on the individual UHPLC, ICP-OES and GC data blocks with related number of latent variables (LVs). Average classification error rates are calculated in a 5-fold cross-validation (CV). Optimal calibration models are bolded. The SO-PLS-LDA model required the extraction of one LV from the UHPLC block, four from the ICP and one from the GC. On the other hand, SO-CovSel required 13 variables: five from the UHPLC chromatograms, seven from the ICP, and one from GC signals. As can be seen from the correct classification rates reported in Table 3, both approaches performed well. In particular, SO-PLS-LDA misclassified only three samples (two from class _Passerina_ and one belonging to class _Trebbiano_) out of eighteen in the test set. Similarly, SO-CovSel-LDA erroneously assigned four samples: one each belonging to class _Passerina_ and to class _Precorino_, and two appertaining to class _Trebbiano_. A graphical representation of the SO-PLS-LDA outcome is reported in Figure 5; in the plot, the samples are projected onto the canonical variate space [38]. All the investigated objects are quite well-divided into the three categories: the first canonical variate allows discriminating samples appertaining to class _Precorino_ (purple squares, at positive values of CV1) and those belonging to class _Trebbiano_ (blue diamonds, at negative values of CV1). On the other hand, objects belonging to class _Passerina_ (red dots) can be distinguished from those appertaining to the other two categories along CV2. From the figure, however, it is possible to notice a slight overlap between class _Passerina_ and the other two categories; this led to some erroneous assignments (highlighted by a black cross). In particular, two misclassified objects belonging to class _Passerina_ were assigned to class _Precorino_, and one _Trebbiano_ sample was predicted as belonging to class _Passerina_. Interestingly, the relatively large intra-class variability of _Passerina_ individuals in the canonical variate space seems to reflect the higher heterogeneity in the sensorial attributes observed for this wine variety compared to the others. By contrast, _Trebbiano_ individuals give rise to a compact cluster, which is in line with the high homogeneity of sensory characteristics within the wines of this variety detected by panelists, whereas the intra-class variability of _Precorino_ samples, according to both sensorial and chemical properties, is between that of the other two wine categories. The possibility that sequential multi-block methods would have provided accurate predictions had its own rationale in the literature. In fact, as mentioned in the introduction,  
Figure 5: SO-PLS-LDA analysis. Wine samples projected onto the space of the two canonical variates (CV1 and CV2). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Classifier**} & **LVs** & \multicolumn{2}{c}{**Classification Rates (External Set)**} & \\ \cline{2-5}  & \((X_{1},X_{2},X_{3})\) & **Class Passerina** & **Class Pecorino** & **Class Trebbiano** \\ \hline SO-PLS-LDA & 1,4,1 & 50.0 & 100.0 & 83.3 \\ SO-CovSel-LDA & 5,7,1 & 75.0 & 87.5 & 66.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Data-block (SO-PLS-DA and SO-CovSel-LDA) models: number of latent variables (LVs) for each block and classification rate on the external prediction set.