## 3 Results
### Diffuse Transmission Spectroscopy Analysis
#### 3.1.5 Comparison of Wavelength Selection Methods on Transmittance PLRR Model  
In this study, four methods were employed for spectral feature wavelength selection, to optimize model performance. These methods were CARS, SPA, MC-UVE, and RF. CARS selects the most critical wavelengths for modeling through adaptive weighting and resampling techniques, reducing redundant features and improving the model accuracy and stability. SPA employs a stepwise projection approach to minimize correlations between variables, optimizing the feature set and enhancing the model interpretability. MC-UVE utilizes the Monte Carlo method, selecting the wavelengths that contribute the most to prediction through multiple random samplings and cross-validation, thereby improving the model accuracy and robustness. RF, inspired by swarm intelligence, randomly optimizes feature combinations and identifies the most informative wavelengths, enhancing the model predictive performance. By integrating these methods, this study aims to select the most representative spectral feature wavelengths, thereby enhancing both model prediction capability and interpretability. These feature selection techniques preserve the integrity of the information while eliminating redundant features in high-dimensional spectral data, thus optimizing modeling outcomes. The modeling effects of spectral feature wavelength selection using these four methods are shown in Figure 7.  
Figure 6: Diffuse transmittance PLRR model established using MSC preprocessing. Figure 7: _Cont_. From the analysis of the data presented in Table 4, it is evident that different feature wavelength selection methods significantly impacted the model performance. Among these methods, CARS behaved as the most effective and notably enhanced both the calibration and prediction capabilities of the model through adaptive weighting of feature wavelengths. Specifically, CARS identified 63 feature wavelengths, achieving a coefficient of determination of 0.98 for the calibration set and 0.97 for the prediction set. The RMSE was 0.58 \({}^{\circ}\)Brix for the calibration set and 0.72 \({}^{\circ}\)Brix for the prediction set. These results indicated that CARS not only optimized feature selection but also substantially improved the overall performance of the model. In comparison, although the SPA also selected 63 feature wavelengths, it achieved a coefficient of determination of 0.94 for the calibration set and 0.95 for the prediction set. However, SPA exhibited higher RMSEs of 1.02 \({}^{\circ}\)Brix and 1.03 \({}^{\circ}\)Brix, indicating limitations in prediction accuracy. The RF method also demonstrated strong performance with 70 feature wavelengths. The coefficients of determination for RF were 0.98 for the calibration set and 0.96 for the prediction set, with RMSE values of 0.52 \({}^{\circ}\)Brix and 0.87 \({}^{\circ}\)Brix, respectively. Although the overall performance of RF was slightly inferior to that of CARS, it still provided high prediction accuracy and model stability. The MC-UVE method, which selected 64 feature wavelengths, showed stability in terms of coefficient of determination and prediction accuracy. However, its RMSE values were relatively high, at 0.67 \({}^{\circ}\)Brix and 0.77 \({}^{\circ}\)Brix. In summary, the CARS method significantly enhanced modeling performance through effective feature wavelength selection, making it the most effective feature selection technique in this study. The detailed results of the feature wavelength selection are shown in Figure 8. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Methods** & **LVs** & **No. of Wavelengths** & \(R_{C}^{2}\) & \(R_{p}^{2}\) & **RMSEC (\({}^{\circ}\)Brix)** & **RMSEP (\({}^{\circ}\)Brix)** \\ \hline CARS & 9 & 63 & 0.98 & 0.97 & 0.58 & 0.72 \\ SPA & 6 & 63 & 0.94 & 0.95 & 1.02 & 1.03 \\ RF & 10 & 70 & 0.98 & 0.96 & 0.52 & 0.87 \\ MC-UVE & 11 & 64 & 0.97 & 0.97 & 0.67 & 0.77 \\ \hline \hline \end{tabular}
\end{table}