## 3 Results and Discussion
### Quadratic Discriminant Analysis  
After undergoing the sequential feature selection process previously described, a subset of four principal components, namely PC3, PC4, PC5, and PC8 is obtained, minimising the error rate of the 6-fold cross validated model to 0.479. As Figure 2 highlights, the fraction of variance relevant for the discrimination between classes refers to short T2 ranging from 10 to 60 ms (PC5), and long T2 (100 to 200 ms) of water protons in solution (PC4). PC3 is characterised by protons with very long T2 (above 800 ms) and is thus associated with bulk water attributable to the mozzarella's exudate contained in the largest pores. This result reflects the water proton populations highlighted in the T2 distributions (Figure 1). On the other hand, PC8 shows a constant increase in the absolute value of PC loadings as a function of the acquisition time, representing what could be a drift in the signal characterised by high noise and apparently not relevant for the structural description of the food matrix. Figure 1: Mean T2 distribution of day 2 samples as function of frozen curd (FC) content. Different FC concentrations are denoted by solid coloured lines. The model's predictions of the cross-validation set and of the independent test set are represented in the confusion matrices reported in Figure 3. Model sensitivity (True Positive Rate) for the cross-validation set is 0.63, 0.54, 0.27, and 0.61 for the classes 0, 15, 30, and 50% FC respectively, while the model sensitivity for the same classes from the independent test set prediction is 0.67, 0.33, 1, and 1. Model specificity (True Negative Rate) for the cross-validation set is 0.86, 0.86, 0.78, and 0.88 for the classes 0, 15, 30, and 50% FC respectively, while model specificity for the same classes from the independent test set prediction is 1, 1, 0.67, and 1. It is remarked that in this case, particular interest is given to the prediction of the 0% FC class, as it is the only class representing unadulterated samples. Thus, evaluating the model performances by focusing on specificity is a better choice for the present classification task than overall accuracy. Figure 3 shows that, in the cross-validation set, four compliant products are mistaken as adulterated (false negatives), while five (out of 37) adulterated products are incorrectly assigned to the complaint PDO class (false positives). Better results are obtained in the independent test set where only one false negative for the 0% FC class was predicted. Figure 4 shows the receiving operator characteristic (ROC) curve for the 0% class, with an area under the curve (AUC) equal to 0.81. This result denotes a fair discrimination ability of the model for that specific class which is also remarked by the model specificity. This result is particularly important for the purposes of the classification task of this study, and considering the number of samples used to build it, the overall prediction performance of the model is satisfactory. Although the performance oriented model would predict a classification between authentic vs. fake products, the latter category is not internally homogeneous. Moreover, the model was built on four discrete categories because the matrix effect is not linearly correlated to the fraction of FC. The confusion matrix shown in Figure 3 clearly shows that the prediction errors occur mainly between contiguous classes. Artificially building a single class with all-fake-samples will force the system to consider homogeneous a class that conversely has the same internal differences as those existing between the authentic product and the one with a lower FC content (i.e., 15%). This generates misleading results. Furthermore, the experimental design that lead to the dataset construction was focused on balancing classification performances and description of the supramolecular structure.