## 3 Results
### Multi-Block Analysis  
Two multi-block classification approaches, namely SO-PLS-LDA and SO-CovSel-LDA, were used to integrate the information in the two spectroscopic data sets into a single model, hoping that this could also lead to better predictions. In the model selection stage, the best pre-processing and the optimal number of latent/original variables to be retained for each block were identified as those resulting in the lowest classification error in a fivefold cross-validation procedure. Specifically, for each block the same four pre-processings already discussed in the case of the SPORT models were tested, and the optimal combination, consistently with the results obtained on the individual spectroscopic data, was found to be second derivative for MIR and first derivative for NIR. The optimal SO-PLS-LDA model included one latent variable from the MIR block and three from the NIR data matrix. On the other hand, three and two original variables were selected from the NIR and MIR blocks, respectively, to build the SO-CovSel-LDA model. Regardless of the data fusion approach used, both models achieved 100% correct classification in both calibration and validation, correctly assigning all the training and test samples. A graphical representation of the classification accuracy of the SO-PLS-LDA model is displayed in Figure 2, where the projection of the training and test samples onto the space spanned by the first LVs extracted from the MIR and the NIR blocks is shown; this representation exploits the sequential multi-block nature of the SO-PLS algorithm allowing one to straightforwardly visualize the separation between the categories and the within-class scatter [24].The accurate model predictions result from the pure Senise (red diamonds) and adulterated (blue squares) samples were clearly separated in space. Moreover, inspection of Figure 2 also allows one to observe how, as it could be expected given the nature of the samples, the within-class variance of the adulterated category is higher than the one of pure Senise. The distribution of the samples also indicates that the information from both blocks is needed to discriminate between the two classes, since the separation occurs along a direction which is not parallel to any of the axes. At the same time, it is also evident that, consistently with the classification results obtained on the individual blocks, the NIR block is more discriminant than the MIR one, as the two classes are more separated along LV1 NIR than on LV1 MIR: indeed, almost all the pure Senise samples have positive scores on LV1 NIR, while the large majority of the adulterated peppers fall at negative values of the component. Figure 2: Sequential and orthogonalized partial least squares linear discriminant analysis (SO-PLS-LDA) analysis: projection of the training (empty symbols) and test (filled symbols) samples onto the sub-space spanned by the first LV extracted from the MIR block (LV1 MIR) and the first LV extracted from the NIR block (LV1 NIR). Legend: pure Senise: red diamonds; adulterated: blue squares. In addition to the excellent classification performances, not only on the training data but, more relevantly, on the test samples, both SO-PLS-LDA and SO-CovSel-LDA models can be interpreted so as to identify what the experimental variables are that contribute the most to the observed discrimination between the investigated categories. Relying on a variable selection algorithm, in SO-CovSel such information results directly from the model building stage, where the most relevant predictors from each block are extracted. On the other hand, in the case of SO-PLS the identification of the variables contributing the most requires a post-hoc analysis of the model parameters, which can be carried out, e.g., by inspecting the values of the variable importance in projection (VIP) scores, as discussed in [32], which was the strategy adopted in the present study.