## 3 Results and Discussion
### Selection Results of Characteristic Wavelengths  
When the data dimension is large, the information is redundant, the subsequent modeling is relatively slow and the robustness is low. Therefore, it is essential to find out those characteristics that are most effective for classification identification among many characteristics, which should have a large quantity of identification information to make the discriminant models easy to classify and should have reliability and independence, so as to achieve the compression of the characteristic space dimension. The meaning of characteristic extraction is such that heterogeneous pattern points are  
Figure 4: Average spectral curve. Figure 5: Modeling analysis results based on full wavelength. further apart in the minimum dimensional characteristic space (larger distance between classes), while similar pattern points are closer together (smaller distance between classes). Lastly, the SNV-processed spectral data is chosen for characteristic wavelengths extraction, and then the final model combination is determined according to the modeling analysis of the characteristic wavelengths. In this experiment, RFA, UVE, and CARS were utilized to extract characteristic wavelengths from the SNV preprocessed spectral data, respectively. Figure 6 shows the selection probability of each characteristic wavelength extracted by RFA, which is acquired by setting the number of iterations N to 1000 and the number of initial variable M to 2. Since the random frog algorithm is based on Monte Carlo (MC) thought, in order to approximate the optimal solution, it needs to be run multiple times and the results are statistically calculated. A total of 50 RFAs were run in this experiment, and the average value of the 50 runs was used as the basis for the final characteristic wavelengths selection. As can be observed from the figure, the majority of the variables have a low probability of being selected, and only a small number of variables have a high probability of being selected. The experimental threshold is 0.5, which is represented by a red horizontal line, and 11 variables whose probability exceeds the threshold were selected as characteristic wavelengths. Table 1 shows the characteristic wavelengths and the corresponding molecular vibration extracted by RFA [29]. The extracted characteristic wavelengths account for 4.51% of the full wavelengths. Figure 7 is the stability analysis of UVE. The number of LOOCV is 315, and the optimal factor number is 10, and the number of wavelengths of random noise added is 244. The vertical black dotted line shows the spectral wavelength variables stability distribution curve to the left and the introduced 244 system noise variables stability distribution curve to the right. The threshold for the stability of variables in this experiment has an upper and lower threshold of \(\pm\)33.9396, which are represented by two horizontal black dotted lines. The 192 wavelength variables between the two thresholds are non-information variables that can be eliminated, and the 52 wavelength variables that exceed the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **NO.** & **Wavelengths (nm)** & **Molecular Vibration** \\ \hline \multirow{6}{*}{RFA} & \multirow{6}{*}{11} & 1078.3 & Second overtone of C-H + Second overtone of C-C \\  & & 1132.3, 1175.8, 1209.2, & \multirow{6}{*}{Second overtone of C-H} \\  & & 1212.5, 1222.5, 1262.3 & \\ \cline{1-1}  & & 1325.0, 1416.6 & \\ \cline{1-1}  & & 1432.8 & \\ \cline{1-1}  & & 1436.1 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The characteristic wavelengths and the corresponding molecular vibration extracted by random frog algorithm (RFA). Figure 6: Selection probability of each wavelength by utilizing random frog algorithm (RFA). threshold are information variables. Finally, 52 characteristic wavelengths were selected by UVE for subsequent modeling analysis. Table 2 shows the characteristic wavelengths and the corresponding molecular vibration extracted by UVE [29].