## 4 Data Processing
### Between-Class Comparison
#### 4.4.3 Statistical Exploration  
Extracting valuable information from a high-dimensional data set consisting of hundreds of chemical features and several sample properties is difficult. To simplify this process, statistical tools must be used to reduce the data dimension. Before applying the statistical tools, peak normalization with internal standards is recommended to reduce the systematic error. Then, an intuitive approach is to apply univariate statistics, such as the Fisher ratio (FR), to filter out features that are not significantly different among the classes. In univariate statistical analysis, all variables are assumed to be independent, and therefore the analysis does not consider interactions among variables. Because of its simplicity and effectiveness, the FR method has been built into mainstream GC\(\times\)GC data analysis software. It is derived from the concept of ANOVA analysis, which compares between-class variance with within-class variance. If the ratio is greater than the F critical value, then the analyte has a significant variation between sample classes [195]. Originally, it was calculated based on the result in the peak table after peak detection. To avoid interference from peak detection error, it has now evolved to image-based comparison, or tile-base FR [172]. A proper tile size selection is important to prevent deteriorated analyte discovery [196]. It is important to mention that many chemicals in the beverage are not independent, so simply applying the FR analysis may discard many relevant features or overlook important features. One should have a scientific background in the sample, knowing the objective of the work and the chemistry relevant to the beverage composition, to supervise the FR test. For example, during taste testing, esteric compounds should not be filtered out even if they do not pass the FR test individually [197].On the other hand, in multivariate statistical analysis, multiple correlated variables can be combined and represented by a new \"latent\" vector. In such a way, the number of studied volatile features is reduced, and the most informative variables are extracted. Then, selected volatile features can be used for modeling the interested biological phenomena. Still, in the presence of more variables than samples, correlation can also arise by \"chance\". Even with multivariate methods, validation and domain-specific knowledge are required to confirm the results of the experiments. Principal component analysis-based (PCA) tools determine the sources of the greatest variance and are widely used in GC\(\times\)GC result exploration [198]. Principal component analysis (PCA) is widely used in the exploration of GC\(\times\)GC results and has been used in many works to characterize wines from different terroris [56; 199] to distinguish the varieties [26], to find chemical markers of wine aging, and also to evaluate the use of different yeasts [35]. PCA can also be applied to graphic data; consider the chromatogram a 3D image and avoid peak identification. With proper binning size applied to the chromatogram, the amount of information for each binned-image comparison is reduced, and the results of image alignment are improved [56]. Other common and useful techniques are discriminant analysis such as partial least squares (PLS-DA) and stepwise linear discriminant analysis (SLDA), which is a supervised multivariate statistical method used for classification purposes and data interpretation, for example. PLS-DA has been used by [PERSON] et al. (2011) to categorize wines according to geographic origin and SLDA to distinguish grape varieties [17; 26; 52]. Recently, machine learning methods have been compared based on wine data [42]. It is expected that artificial intelligence (AI) technologies will be applied to mining GC\(\times\)GC data to facilitate not only feature selection but also feature annotation.