## Classification
### Discriminant Techniques
To overcome this limitation, one can perform a proper selection of these descriptors (via, e.g., step-wise algorithms) [103], apply LDA to the scores resulting from a preliminary PCA modelling of the collected data in what is called PCA-LDA [104; 105; 101] or resort to regularized versions of LDA, like in Regularized Discriminant Analysis (RDA) [106; 107; 108; 109; 110; 111]. While, on the one hand, such approaches are capable of stabilizing the LDA solution against collinearity, on the other hand, some of them might suffer from similar drawbacks as seen before for PCR [104; 105; 112]. Alternatively, one can think of classification as a regression problem in which the class belonging of a sample (i.e., the dependent variable) is to be estimated from the set of (independent) variables returned by a particular analytical platform (e.g., a spectrum). Similarly to what was outlined in Section 3, such an estimation can be carried out by an extension of PLS named Partial Least Squares Discriminant Analysis (PLSDA) [112; 113]. PLSDA regresses the entire data matrix \(\mathbf{X}\) on a dummy binary-coded response array, say again \(\mathbf{Y}\), made up of a set of piled \(Z\)-dimensional row vectors, constructed so that, if their corresponding objects/samples are members of the \(z\)-th class, they have a 1-value in their \(z\)-th entry and 0-values in all the other ones. For instance, in a 2-class scenario, samples belonging to the first category will be described by the dependent vector [1 0], while samples belonging to the second one by the vector [0 1]. Notice that the model structure in Equation (22) applies also in this case and, thus, whenever new objects/samples become available, their projection coordinates onto the PLS latent variables,as well as their **Y**-predicted values, can be retrieved as shown in Section 2. The class assignation can be finally carried out based on an LDA model constructed either on PLS scores of training objects (this approach is also known as PLS-LDA [112; 114; 115]) or on their **Y**-predicted values, according to a highest-prediction rule or to a higher-than-a-threshold prediction rule [116]. As for PLS, more complex variants of PLSDA are available for coping with strong non-linear relationships existing between **X** and **Y** (e.g., Locally Weighted PLSDA--LW-PLSDA [117]--Kernel-PLSDA--K-PLSDA [118; 119; 120]). Support vector machines and artificial neural networks can also be used for the resolution of classification-related problems [83; 91; 121; 122]. For the particular type of problems they make it possible to tackle, discriminant methods have had a long history in the field of food quality assessment and control (see Table 1). LDA, QDA, linear and non-linear PLSDA, support vector machines and artificial neural networks have been broadly used to discriminate foodstuff of different origins [123; 124], different varieties [117; 125; 126], different technological properties [127], different purity degree [128], exhibiting different genotypes (i.e., transgenic/non-transgenic) [129] or affected by different diseases [130; 131]. PLSDA has been applied, for example, to NIR spectra of pistachios for their geographical authentication making it possible to highlight that seeds from Turkey and USA show a typical absorption behavior between 8000 and 9000 cm\({}^{-1}\) (second overtone of methylenic stretching vibrations) [124] and to UV-Vis spectra of ale beers brewed by distinct producers pinpointing minimal variations in the tone and intensity of their color which could indirectly influence customer perception [132].