## Classification
### Modelling Techniques  
Contrarily to discriminant techniques, modelling approaches are capable of capturing similarities among samples belonging to the same category [97; 133]. They basically define a multivariate boundary \begin{table}
\begin{tabular}{c c c} \hline \hline
**Aim** & **Method** & **Reference** \\ \hline Exploration of apple varieties & PCA & [32] \\ Beer storage monitoring & PCA & [33] \\ Adulteration detection of Camellia oils & PCA & [34] \\ Chemical characterization of Mediterranean olive oils & ICA & [35] \\ Chemical characterization of honey samples & ICA & [36] \\ Chemical characterization of soft drinks & ICA & [36] \\ Determination of land content in chocolate samples & PLS & [92] \\ Quantification of turmeric aduliteration in egg-pasta & PLS & [93] \\ Straw wine quality parameter prediction & PLS & [94] \\ Sensory characterization of _Trentingrana_ cheese & PLS & [95] \\ Egg content quantification in dried egg-pasta & Local PLS & [76] \\ Characterization of PDO Chianti Classico olive oil & LDA & [123] \\ Determination of the geographical origin of pistachios & PLSDA & [124] \\ Classification of rice varieties & LW-PLSDA/K-PLSDA/Artificial & [117; 125] \\ Classification of honey samples & PLSDA & [126] \\ Technological classification of egg white powders & PLSDA & [127] \\ Discrimination of distillates & PLSDA & [128] \\ Classification of tomato genotypes & LDA/PLSDA/Support vector machines/ & [129] \\ Olive fruit classification & QDA & [130] \\ Insect infestation detection in stored rice & PLSDA & [131] \\ Characterization of Italian craft beers & PLSDA & [132] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Application examples of exploratory, regression and classification analysis of spectroscopic data in the field of food science. PDO, PCA, ICA, PLS, LDA, PLSDA, LW-PLSDA, K-PLSDA and QDA stand for Protected Designation of Origin, Principal Component Analysis, Independent Component Analysis, Partial Least Squares, Linear Discriminant Analysis, Partial Least Squares Discriminant Analysis, Locally Weighted Partial Least Squares Discriminant Analysis, Kernel-Partial Least Squares Discriminant Analysis and Quadratic Discriminant Analysis, respectively. for each considered class, which delimits a specific region of the multidimensional space of the original descriptors where objects proceeding from it are likely to be found. If an analyzed sample falls within this region, it is assigned to the respective class, otherwise it is considered to be a class outlier and rejected as such [134; 135]. A fundamental aspect that needs to be taken into account here is that categories are treated and handled separately and that an individual model is constructed for every one of them. Subsequently, (i) modelling methodologies can easily be applied in scenarios in which a unique class of interest exists (a common contingency in food traceability or authentication studies), and (ii) new objects can be predicted as members of one, none or multiple classes also in the light of the fact that the various class spaces do not necessarily have to cover completely the whole original variable space [136]. Given their characteristic nature, class modelling strategies can all be regarded as outlier detection methods. Nonetheless, mainly depending on the _outlyingness_ criterion adopted, such strategies can exhibit different advantages and disadvantages and be more or less suitable to be applied in certain situations rather than others. Due to the flexibility that the selection of this outlyingness criterion guarantees, a plethora of class modelling approaches have been proposed throughout the last 45 years. Among those appearing in the chemometric literature (see Table 2), probably the most commonly exploited since their development are UNEQal class spaces (UNEQ [137; 138]) and Soft Independent Modelling of Class Analogy (SIMCA [139; 140]). UNEQ was introduced by [PERSON] and [PERSON] in 1986 and constitutes the modelling version of QDA.