## 3 Results and Discussion
### Fingerprinting for Saffron Authenticity
#### 3.1.2 Statistical Analysis to Reveal Adulterated Saffron Aqueous Extracts Univariate Analysis
The samples of authentic saffron presented chiefly predominance of crocins (buckets at 1.79, 1.87, 5.63, 6.15, 6.43, and 6.47 ppm) and a shift of the formic acid signal (buckets at 8.43 ppm). Figure 2: Results of the hierarchical clustering heat map performed on the normalized data (distance measure using _Correlation_, and clustering algorithm using _Complete_). Each colored cell on the map corresponds to a concentration value in the data table, with samples in columns and metabolites in rows. The belonging class of samples is indicated as red and green squares for adulterated saffron (AS) and authentic one (PS), respectively. Supervised Multivariate Analysis: Partial Least Squares Discriminant Analysis (PLS-DA)  
Aiming at developing a model to discriminate the adulterated safron samples from the authentic ones, PLS-DA was applied to the data matrix obtained from the binned and pre-processed spectral data. The model presented eight components, though the first seven components were selected as the optimal number of components for classification according to a 10-fold cross-validation method. To estimate the predictive ability of the model, the performance measure, Q2, was calculated via cross-validation (CV). In each CV, the predicted data were compared with the original data, and the sum of squared errors was calculated. The prediction error was then summed over all samples (Predicted Residual Sum of Squares or PRESS). For convenience, the PRESS was divided by the initial sum of squares and subtracted from 1 to resemble the scale of the R2. A model characterized by good predictions and without overfitting should have low PRESS or high Q2, as in the case of the PLS-DA model developed here (see Figure S6 in Supplementary Materials for further details). The PLS-DA model was validated through a permutation test upon passing a set of 1000 permutations and testing the prediction accuracy during training. As a result, the observed statistic \(p\)-value was lower than 0.001, confirming the good predictive performance of the developed model (see Figure S7 in Supplementary Materials for further details). The first four components exerted the highest contribution with an explained variance of 62.5% (see Figure S8 in Supplementary Materials for further details). Indeed, the PLS-DA scores plot between Component 1 and Component 2 clearly shows two clusters along Component 1 with an explained variance of 14.4% (Figure 3a). The analysis of the Variable Importance in Projection (VIP) was performed to obtain insights into the variables, and, thus, the metabolites, which mostly contributed to the observed distribution of safron samples in the PLS-DA scores plot. Indeed, VIP represents a weighted sum of squares of the PLS loadings considering the amount of explained Y-variation in each dimension. As a result, a pool of 66 variables with VIP \(>\) 1 on the Component 1 was identified (see Table S3 in Supplementary Materials for the full list). A deeper look into the top 15 VIPs (Figure 3b), revealed that crocin represented the main metabolite contributing to the clustering of the authentic saffron samples which were characterized by a higher content of this compound. Such a result agrees with the information obtained from the univariate data analysis of the same aforementioned samples. On the other hand, the group of adulterated safron samples presented a higher content of saccharides, like fructose and glucose. A visual inspection of the spectra of authentic and adulterated safron samples confirmed the results of the class discrimination since some noticeable variations were observed in the spectral regions containing the signals ascribed to the aforementioned metabolites. Specifically, the content of crocin was relatively higher in the samples of authentic safron (Figure 4, blue spectrum), while fructose was more abundant in the samples of safron adulterated with safflower (Figure 4, red spectrum).