## 3 Overview of Chemometric Tools Applied in the Authentication of Gr and WB GIs  
In the analytical strategies for the authentication of Gr and WB GIs, an important role is played by the chemometrics tools used to process the large datasets produced by the application of state-of-the-art analytical methods. Although there are no strict guidelines for the selection of the multivariate statistical technique, it is possible to define a rational scheme (Figure 1). Initially, it is essential to establish whether the collected data can effectively discriminate samples within the different target classes. To this aim, PCA is one of the most frequently applied tools as it can reduce the dimensionality of a large amount of data by projecting samples into a low-dimensional space, allowing the identification of sample groupings and patterns [88]. While PCA is commonly used for two-way data (such as those generated from conventional chromatographic methods, for example), PARAFAC may be the technique of choice for three-way data obtained, for instance, from EEM. PARAFAC can, in fact, decompose the information into several components that more specifically describe the variability of the entire dataset [89]. Another tool, frequently used for exploratory data analysis in Gr and WB authentication studies, is the HCA. It allows similar observations to be grouped into clusters based on the values of different variables for each object [88].  
Once explored, the data can be classified or calibrated. Both discriminating and class modeling approaches have been considered in classification studies of Gr and WB. Among discriminating tools, mainly LDA and PLS-DA have been applied. LDA calculates linear combinations of the original variables to maximize the separation between the different categories and minimize the variance within each category. PLS-DA applies regression to predict the category of a sample [89]. Indeed, SIMCA is a class modeling approach that determines significant principal components to predict the class of samples based on their distance from the model of each class [90]. The purpose of multivariate calibration methods, instead, is to determine correlations between the responses and the independent variables. MLR and PLS are often used for this purpose in Gr and WB GI authentication studies. In multi-platform authentication methods, SO-PLS-LDA and SO-CovSel-LDA were frequently carried out to obtain single classification models by the fusion of data extracted from  
Figure 1: Visual overview of chemometric tools applied in the authentication of Gr and WB GIs.  
different analytical techniques. Furthermore, the last few years have seen rapid growth in the use of machine learning algorithms to build classification and prediction models.  
After statistical modeling, the determination of model performance and evaluation of the existence of possible overfitting [90] is generally carried out. For this purpose, cross-validation and external validation have been the most applied in Gr and WB GIs. The former involves separating the dataset into calibration and validation sets, while the latter is performed when using independent test sets. Correct classification rates are the most frequently used parameters to assess the performance of authentication methods in the works presented in this review. In multivariate calibration models, the performance evaluation includes the coefficient of determination (R\({}^{2}\)), which provides a measure of the good fitting of the model, and the root mean square calibration and prediction errors (RMSEC and RMSEP), which are applied to estimate the prediction capability of the models.