## 3 Results and Discussion
### Comparison of Different Variable Selection Algorithms
The variables in the Raman fingerprint region were neglected. VIP selected variables at both ends of the spectrum (less than 500 cm\({}^{-1}\) and more than 3000 cm\({}^{-1}\)), which severely affected the model performance. The spectral variables selected by UVE were relatively decentralized. Different spectral regions were involved even in the Raman-silent regions. The spectral variables selected by MWPLS were mainly in the Raman fingerprinting region and C-H stretching region. GA and RF were significantly different from other variable selection algorithms, and the selected spectral variables were so scattered that it was impossible to see the variable order. Figure 4: Model cross-validation results with different numbers of variables selected by six variable selection algorithms. (**A**) Glucose, (**B**) lactate, (**C**) viable cell density, and (**D**) ammonium ion. In summary, the performance of variable selection algorithms is different. If an inappropriate variable selection algorithm was used, the performance of Raman-based models would be reduced. Therefore, the variable selection algorithm should be selected and used carefully. For the Raman-based models in the cell culture process, the above results show that RF and GA can significantly reduce the model prediction error, and the number of selected variables is from 30 to 300. The spectral variables selected by MWPLS are more reasonable than PCC, VIP, and UVE, and the model performance is improved to a certain extent. The number of spectral variables selected by MWPLS is large. The variables selected by PCC, VIP, and UVE cannot be explained, and the model performance is not ideal. When MWPLS was used to select 800, 2900, 800, and 100 variables for Gluc, Lac, VCD, and NH\({}_{4}\)+, the minimum RMSECV obtained was 0.19 g/L, 0.092 g/L, 0.43 \(\times\) 10\({}^{6}\) cells/mL, and 0.92 mmol/L, respectively. When GA was used to select 100, 200, 300, and 90 variables for the four components, the minimum RMSECV obtained was 0.19 g/L, 0.082 g/L, 0.040 \(\times\) 10\({}^{6}\) cells/mL, and 0.73 mmol/L, respectively. When RF is used to select 80, 200, 60, and 100 variables for the four components, the minimum RMSECV obtained is 0.13 g/L, 0.051 g/L, 0.28 \(\times\) 10\({}^{6}\) cells/mL, and 0.48 mmol/L, respectively. Table 4 listed the model calibration and prediction results of Gluc, Lac, VCD, and NH\({}_{4}\)+, using MWPLS, GA, and RF variable selection algorithms. Although these variable selection algorithms could effectively reduce RMSECV according to the cross-validation results, not every model performance was improved for the external validation set. For example, the use of RF reduced model performance by 8% and 21% for glucose and viable cell density, respectively, and the use of MWPLS reduced model performance by 36% for ammonium ions. This may be caused by the large noise included in the selected variables. Figure 5: Ranking of variables selected by different variable selection algorithms. The color changing from yellow to green to blue represents the decreasing order of spectral variable selected by variable selection algorithms. Specifically, yellow indicates the top variable, and blue indicates the bottom variable. According to Section 3.1, in order to select variables more effectively, some irrelevant and disturbed variables can be avoided by spectral region selection. We first defined the spectral region so that the variables were limited in the 600-1800 cm\({}^{-1}\) and 2800-3000 cm\({}^{-1}\) regions. Based on this, MWPLS, GA, and RF were used to select spectral variables, and the results of the model are shown in Table 5. After spectral region selection, MWPLS, GA, and RF effectively improved the model accuracy of each component. The R\({}_{\text{C}}\) and R\({}_{\text{P}}\) of all models was greater than 0.93. MWPLS improved the model performance by 37-60% by selecting 600-1300 variables. GA improved the model performance by 25-73% by selecting 100-400 variables. RF improved the model performance by 12-65% by selecting 100-300 variables.