## 4 Data Processing
### Background Correction  
To accurately identify and quantify analytes, background correction is required. This long-standing problem was first reported in the 1960s [147]. The central idea is to try to remove the signals that are not coming from the ionization of the molecules and that are present either as high-frequency noise or as a smooth background signal. Background correction can be divided into three steps: electronic noise removal, signal smoothing, and baseline correction. Electronic noise may be dominant in GC\(\times\)GC data, so it should be removed at the beginning. It is generally represented as a low-intensity signal, and its removal only requires estimating the signal intensity and setting a threshold. Signal smoothing can be achieved with a low-pass filter. The last step is the baseline correction. Since the stationary phase in the GC column is not thermally stable, the baseline drift caused by stationary phase leakage with temperature and flow rate changes needs to be corrected. Baseline-drift corrections are usually performed by curve fitting or smoothing strategies. Both methods predict the baseline of the entire chromatogram from the fitted curve of the non-peak signal and then correct for it. Common fitting methods are polynomial fitting and least-squares fitting [148]. Many background correction methods have been developed for GC\(\times\)GC, such as direct subtraction of mean blanks, local minima values (LMV), asymmetric weighted least squares (AWLS), trilinear decomposition (TD), linear least squares curve fitting methods coupled with moving average smoothing combined with robust orthogonal background correction (ROBC), and singular value decomposition (SVD). Some of them are parametric models (LMV, TD, ROBC), and others are non-parametric (AWLS, SVD). Parametric models assume that the background consists of a fixed combination of terms and can be modeled by applying simple or high-dimensional linear regression. On the contrary, the nonparametric approach does not preset the number of parameters to fit the model. Instead, suitable model parameters are selected based on the experimental data from the baseline. However, both parametric and non-parametric models inevitably make assumptions based on standard chromatograms, which may lead to problems in extreme cases. When a large number of peaks are concentrated in a certain area or even some peaks are connected together, which is common in beverage VOC analysis, the peak signal and background signal become difficult to distinguish [149]. Baseline correction is becoming increasingly difficult, and incorrectly predicted baselines can result in the elimination of true peak signals or the mixing of residual signals with the baseline. A few papers illustrate the mathematical premise of the algorithm in terms of the experimental chemistry of the chromatographic data and test the performance of the model under different extreme conditions, such as heavy co-elution, column saturation, detection saturation, and their coexistence. This makes it difficult for the analyst to choose the most appropriate method based on the experimental chromatogram. In our opinion, the local minima approach respects the experimental data the most. It is more suitable for chromatographic data from complex beverage samples where imperfect chromatographic signals such as saturation may be present [150].