## 3 Results and Discussion
### Comparison of Different Variable Selection Algorithms  
A well-designed variable selection algorithm has the potential to preserve model accuracy, simplify the model, and significantly enhance computational speed. Figure 4 elucidates the predictive outcomes achieved through the utilization of different numbers of variables for each variable selection algorithm. No matter which variable selection algorithm was used, when the number of selected variables was less than 10, the model error was large. When the number of selected variables was more than 1000, RMSECV changed less as the number of spectral variables changed. When the number of variables selected by VIP was less than 2700, the RMSECV obtained was larger than that of whole spectra, indicating that VIP could not effectively select spectral variables for Raman-based models in cell culture. GA, RF, and MWPLS could better improve the model performance for each component, and RF was better than GA and MWPLS. For RF, when the number of selected variables was less than 30, the RMSECV gradually decreased with the increase in the number of variables; when the number of selected variables was more than 30 and less than 300, the RMSECV was small and did not change much with the change in the number of spectral variables; and when the number of selected variables was more than 300, the RMSECV increased with the increase in the number of variables. GA was similar to RF, except that the RMSECV was generally higher than that obtained by RF. MWPLS tends to select a larger number of spectral variables to obtain a smaller RMSECV. The RMSECV obtained by UVE changed into an S-shape with the increase in the number of selected variables, and the RMSECV obtained was relatively small when the number of selected variables was from 300 to 1000. For PCC, when the number of selected variables was less than 40, the model prediction error was basically unchanged, with the increase in the number of selected variables; when the number of selected variables was 40-300, the model prediction error gradually decreased with the increase in the number of variables; \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Component**} & \multirow{2}{*}{
\begin{tabular}{c} **Spectral** \\ **Region** \\ \end{tabular} } & \multirow{2}{*}{**N**} & \multirow{2}{*}{**LV**} & \multicolumn{2}{c}{**Calibration**} & \multicolumn{2}{c}{**Prediction**} & \multirow{2}{*}{**PI (\%)**} \\ \cline{5-6}  & & & & **RMSEC** & & **R\({}_{\rm C}\)** & & **RMSEP** & **R\({}_{\rm P}\)** \\ \hline \multirow{4}{*}{Gluc} & FP8 + CHS0 & 1500 & 9 & 0.11 & 0.98 & 0.18 & 0.97 & 17 \\  & FP17 + CHS0 & 2400 & 14 & 0.09 & 0.99 & 0.17 & 0.97 & 20 \\  & FP5 + CHS2 & 1400 & 7 & 0.13 & 0.98 & 0.14 & 0.98 & 34 \\  & FP8 + CHS0 & 1500 & 9 & 0.06 & 0.99 & 0.07 & 0.95 & 64 \\ Lac & FP17 + CHS0 & 2400 & 15 & 0.03 & 0.99 & 0.07 & 0.95 & 64 \\  & FP5 + CHS2 & 1400 & 5 & 0.06 & 0.98 & 0.07 & 0.94 & 61 \\  & FP8 + CHS0 & 1500 & 8 & 0.28 & 0.98 & 0.25 & 0.99 & 48 \\ VCD & FP17 + CHS0 & 2400 & 12 & 0.29 & 0.98 & 0.41 & 0.98 & 13 \\  & FP5 + CHS2 & 1400 & 9 & 0.27 & 0.99 & 0.26 & 0.99 & 44 \\  & FP8 + CHS0 & 1500 & 7 & 0.55 & 0.99 & 0.61 & 0.99 & 30 \\ NH4\({}^{+}\) & FP17 + CHS0 & 2400 & 12 & 0.47 & 0.99 & 0.66 & 0.99 & 24 \\  & FP5 + CHS2 & 1400 & 7 & 0.50 & 0.99 & 0.52 & 0.99 & 39 \\ \hline \hline \end{tabular} N represents the number of selected variables.  
\end{table} 
Table 3: Calibration and prediction result of models with three different spectral regions. and when the number of selected variables was greater than 300, the RMSECV obtained by the model had little difference. Taking glucose for example, the ranking of spectral variables selected by these variable selection algorithms is plotted in Figure 5. The order of variables selected by different variable selection algorithms was quite different. PCC initially selected variables in the spectral ranges of 200-500 cm\({}^{-1}\) and 2800-3000 cm\({}^{-1}\) and then selected variables in the range of 1800-2500 cm\({}^{-1}\).