## 2 Data Exploration
PCA and ICA have been both extensively used in the field of food characterization (see Table 1); by way of illustration, PCA has been coupled to (i) high-resolution \({}^{1}\)H Nuclear Magnetic Resonance (NMR) spectroscopy for the discrimination of three apple varieties (Bramley, Russet and Spartan), making it possible to spot significant variations in their malic acid and sucrose content [32]; (ii) synchronous fluorescence spectroscopy for monitoring changes in the flavin composition of beer during storage either under light exposure or in darkness [33]; and (iii) Attenuated Total Reflectance Mid-InfraRed (ATR-MIR) spectroscopy and diffuse reflectance NIR spectroscopy in a feasibility study on the detection of soybean oil adulteration in Camellia oil samples [34]. Conversely, due to its particular methodological basis, ICA has mainly been applied to extract the individual spectral contributions and proportion profiles of certain classes of analytes constituting heterogeneous food matrices, e.g., primary oxidation and polyphenic compounds, locopherol, carotenoids and chlorophylls in extra virgin olive oils [35], or fructose, sucrose and glucose in soft drinks [36]. Sometimes, in the context of unsupervised data analysis, one may be interested in having information about the different degrees of similarity/dissimilarity among samples or, more specifically, on whether the distribution of individuals enables the identification of groups or clusters. Clusters correspond to sets of observations which are more similar to one another than they are with respect to all the remaining objects. In this regard, the search for possible clusters of samples is the objective of the so-called clustering techniques, whose basic idea is that similarity among individuals can be inversely related to a distance measure in a multivariate space [37; 38]. Based on this concept, clustering techniques can operate non-hierarchically (partitioning methods) or hierarchically. The former [39], encompassing also the popular \(k\)-means algorithm [40], distribute the samples among a pre-defined number of groups (that can be either known a priori or inferred empirically from the data under study); a sample is basically placed in the cluster with the closest barycenter. They are relatively straightforward, but they suffer from the limitation of needing the number of groups, \(k\), to be defined beforehand. Conversely, as the name suggests, hierarchical approaches proceed iteratively through successive agglomerations of smaller clusters into larger ones [41]--the same approach can be operated top down by progressively dividing larger clusters into smaller ones, but it is more rarely used. Every object is initially assumed to constitute a separate group of observations (_singleton_) and, afterwards, at each iteration, the two most similar groups are joined into a single ensemble. The procedure continues until a certain stopping criterion is met or when all the samples are gathered into a unique cluster. Hierarchical approaches provide more detailed insights into the relations between individuals and/or groups of individuals, but they have the disadvantage that, due to the nature of the agglomeration process, the identification of the most plausible number of clusters may not be easy. The interested reader can find more details on clustering techniques in [37; 38; 42].