## 3 Results and Discussion
### Single- and Multi-Block Varietal Classification  
The data set available for the classification analysis is made of three data blocks: UHPLC signals (\(X_{1}\)), ICP-OES data (\(X_{2}\)), and GC chromatograms (\(X_{3}\)). The absolute peak areas of the detected analytes in UHPLC (\(X_{1}\)) and GC-MS (\(X_{3}\)) chromatograms were considered as variables in the respective blocks. All the calculations were run in Matlab 2015a (The Mathworks, Natick, MA, USA) using in-house functions. Prior to the creation of the classification models, samples were divided into a training and a test set using the Duplex algorithm [35] in order to perform external validation. This  
Figure 4: Mean sensory profiles of _Pecorino_ (PE), _Passerina_ (PA), and _Trebbiano d’Abruzzo_ (TR) wines. process aims at estimating the predictive error provided by the models. Basically, a portion of the available samples (at least the 30% of the total) is left as an external test set and treated as if it were unknown. Once the model is built, the validation set is predicted, and, since the class membership of these objects is known, the predictive error can be estimated. The application of the Duplex algorithm ensures the representativeness of the two sets. To reorganize the objects in subsets while simultaneously taking into account the variation present in all the blocks, the procedure described in [36] was applied. Briefly, a Principal Component Analysis model was calculated on each (mean-centered) data matrix and five components (PCs) were extracted by \(X_{1}\), \(X_{2}\), and \(X_{3}\). These PCs were row-augmented (obtaining \(T_{sup(4\gamma\times 15)}\)) and the Duplex algorithm was applied on the resulting matrix \(T_{sup}\). The outcome of this procedure led to the reorganization reported in Table 1.  
Firstly, classification models were calculated on the individual data matrices by PLS-DA. Depending on the nature of the data, different preprocessing approaches have been tested: mean-centering (MC), autoscaling, probabilistic quotient normalization (PQN) [37], and logarithm base 10 (Log10). The model parameters (i.e., the most suitable pretreatment and the number of latent variables (LVs) to be extracted) have been defined into a five-fold cross-validation procedure; the results are reported in Table 2. The optimal PLS-DA models (i.e., those leading to the lowest average classification error in cross-validation, bolded in Table 2) were than applied to the test set (preprocessed accordingly). PLS-DA analysis on (mean-centered) UHPLC data provided correct classification rates of 50.0%, 75.5%, and 83.3% for samples belonging to class _Passerina_, class _Pecorino_, and class _Trebbiano_, respectively. The PLS-DA model created on the ICP-OES data (preprocessed by Log10) correctly assigned 40.0% of samples supertaining to class _Passerina_, 75.0% of the objects from class _Pecorino_, and 50.0% of _Trebbiano_ samples; the PLS-DA model calculated on mean-centered GC data led to correct classification rates of 25.0%, 62.5%, and 83.3% for samples belonging to Class _Passerina_, Class _Pecorino_, and Class _Trebbiano_, respectively. Next, SO-PLS-LDA and SO-CovSel-LDA models were built on the data preprocessed in agreement with the outcomes of PLS-DA analysis; the results are reported in Table 3. As expected, the data fusion strategies provided better results (from the prediction point of view) than the individual-block analysis. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Training Set (_n. Samples_)} & \multicolumn{5}{c}{**Test Set (_n. Samples_)**} \\ \hline _Passerina_ & _Pecorino_ & _Trebbiano_ & Tot. & _Passerina_ & _Pecorino_ & _Trebbiano_ & Tot. \\
7 & 10 & 11 & 28 & 4 & 8 & 6 & 18 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Class memberships of the wine samples in the training and the test set.