## 2 Processing of HS-SPME-GC-MS Data on Wine Volatiles by Multivariate Statistics
### Principal Component Analysis  
Principal Component Analysis (PCA) is a multivariate data statistical analysis that provides a reduction in data set dimensionality by finding linear combinations of the original independent variables, called principal components, which explain the maximum of data-set variance. Principal components are orthogonal latent variables generated from the correlation or covariance matrices of data; original data projections along the axes identified by principal components are called scores. The full set of principal components can be as large as the original set of variables, but most of the original data variance is typically concentrated in a limited number of principal components. Similarities or differences between the original multivariate data can thus be usually appreciated on a simple two-dimensional scatterplot, called a score plot, reporting the scores based on the first two principal components. Moreover, by plotting the contribution of the original variables to the principal components (loading plots) it is also possible to understand how the original variables contribute to the similarity or to the difference between original samples. PCA is used as a tool for screening, extracting, and compressing multivariate data [24; 26; 27; 28; 29]. In the context of the HS-SPME-GC-MS analysis of wines' volatile compounds, PCA is one of the most useful multivariate techniques to assess the authenticity of wines [47; 48]. As an example, it was adopted to distinguish 22 red wines produced in the four main wine regions in France, starting from data obtained from both sensory and VOCs analyses [49]. Recently, the combined use of the ANOVA technique to select the most \"class-distinguishing\" chromatographic peaks area and the subsequent PCA analysis allowed [PERSON] et al. [50] to cluster white wines (_Grillo_ wines) produced in different areas of Sicily and to determine geographic differences in their volatiloma. [PERSON] et al. [51] investigated the correlation between the volatile composition and sensory properties in Spanish _Alburito_ wines, through PCA. Following this, the multivariate regression approach based on the use of PLS and PCA was used by [PERSON] et al. [52] to study the correlation between sensory data and volatile compounds, in Pinot Blanc, in order to use chemical fingerprints to obtain a prediction of the sensory profile of the wine. PCA analysis was also used to evaluate the impact of different yeast strains on the wine quality and on the progress of the fermentation process. As an example, [PERSON] and co-workers [53] applied PCA to identify the volatile compounds that best discriminated wines produced by yeast strains selected in the two different areas, i.e., north and south Salento in the Apulia region of Italy. In addition, PCA was used for highlighting the differences among sparkling wines produced using different autochthonous yeast strains for the secondary fermentation step [54]. PCA coupled with discriminant analysis (DA) analysis has recently been used as a chemometric tool to identify the ageing process (barrel- or chip-aged) the wine undergoes, by selecting key volatile molecules detected via GC-MS [55]. Through a PCA-based elaboration of data on phenolics and volatile compounds, [PERSON] et al. [56] highlighted that there were significant differences between wines aged in control and new barrels, while fewer clear-cut differences were detected between wines aged in barrels produced with different bending/toasting protocols. More recently, PCA was applied, in conjunction with Hierarchical Cluster Analysis, to a set of 103 volatile compounds identified by HS-SPME-GC-MS, indicating peculiar features in the VOC profile related to the geographical origin of nine red wines produced in Brazil [57]. [PERSON] et al. [58] used PCA to assess the effect of different tank materials on the profile of VOCs of a _Sangiovese_ red wine obtained using HS-SPME-GC-MS.