## 2 The Tools--Chemometrics and Vibrational Spectroscopy  
### Chemometrics  
Chemometrics may be defined as the combination of algebra, mathematics and statistical analysis techniques to analyse and process data [37; 38; 39; 40; 41; 42]. It allows for multivariate analysis which is incredibly useful for processing large datasets derived from food analysis, particularly instrumental analysis (e.g., spectroscopy) [37; 38; 39; 40]. The different methods and techniques allow the analyst to isolate and interpret pertinent information from complex datasets, illustrate patterns within the data, and develop calibration and validation models [37; 38; 39; 40]. The application of chemometric methods has become more common in recent years as computing power and the availability of chemometric software packages has increased [41; 42]. The chemometric method or technique used in this type of applications (e.g., authenticity, traceability, provenance) can be divided into unsupervised (e.g., samples can be classified without any prior knowledge) or supervised (e.g., prior knowledge about the sample or dataset is required) [37; 38; 39; 40]. While unsupervised methods are useful for the clustering of samples, i.e., determining the internal grouping in a set of unlabelled data, they are not suitable for predicting the category of unknown new objects, which would require supervised methods. In most cases, supervised classification models must be developed using a training set of samples that have a well-definedcategory or property. The overall performance of the model might be evaluated by contrasting the predicted with the true category samples (validation) [37; 38; 39; 40; 41; 42; 43; 44; 45].  
Principal component analysis (PCA) is the most widely used variable-reduction method utilised in chemometrics. It is a versatile method of providing a clear overview of complex multivariate data and illustrating relationships between variables and samples, showing the existence of clusters or patterns in the data, while also highlighting outliers (see Figure 1) [43; 44; 45]. In addition to PCA, other classification or pattern recognition techniques have been applied [46; 47]. Some of the most common used discriminant analysis methodologies (e.g., supervised and unsupervised) include cluster analysis, K-nearest neighbours (k-NN), linear discriminant analysis (LDA), factorial discriminate analysis (FDA), partial least squares discriminant analysis (PLS-DA), quadratic discriminant analysis (QDA), artificial neural networks (ANN), soft independent modelling of class analogy (SIMCA), and more recently machine learning methods and techniques such as support vector machines (SVM) [46; 47].  
As well as the algorithms or chemometric method used to develop an application, pre-processing of the spectra is also required in most cases [46; 47]. For example, derivatives (e.g., first and second) are often used to reduce the broad overlapping bands that exist in the spectra, in particular in near infrared (NIR) spectroscopy [36; 37; 38; 40; 46; 47]. Pre-processing techniques also aid in resolving any baseline shift build in the raw data [36; 37; 38; 40; 46; 47]. Other pre-processing methods widely used in spectroscopy are smoothing, detrending, standard normal variate (SNV) and multiplicative scatter correction (MSC). More details about these techniques can be found in the scientific literature in this topic [36; 37; 38; 40; 46; 47].