## Results
### VIS/NIR Spectrometer for TSS Detection of Orange
#### 3.1.3 Feature Wavelength Extraction  
Each spectrum of data has 2151 features (250-2500 nm). However, not all features are helpful in TSS detection modeling. Some low relation features can even interfere with the detection ability. It is necessary to eliminate non-useful features and keep useful features to improve the computation efficiency and accuracy. For this reason, MI was used to evaluate the correlation between each feature and the TSS value. The range of MI is 0 to 1. The larger the MI, the higher the correlation. MIs between features and TSS value are shown in Figure 4. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Data Processing Method** & **DP 1** & **DP 2** & **DP 3** & **DP 4** & **DP 5** & **DP 6** & **DP 7** & **DP 8** \\ \hline R\({}^{2}_{\text{cal}}\) & 0.9852 & 0.7372 & 0.9101 & 0.9996 & 0.6486 & 0.9250 & 0.9386 & 0.9110 \\ R\({}^{2}_{\text{val}}\) & 0.0932 & 0.1047 & 0.4001 & 0.0687 & 0.1336 & 0.3236 & 0.0063 & 0.0077 \\ \hline
**Data Processing Method** & **DP 9** & **DP 10** & **DP 11** & **DP 12** & **DP 13** & **DP 14** & **DP 15** & **DP 16** \\ \hline R\({}^{2}_{\text{cal}}\) & 0.9919 & 0.9386 & 0.8992 & 0.9982 & 0.9807 & 0.7285 & 0.8981 & 0.8952 \\ R\({}^{2}_{\text{val}}\) & 0.2593 & 0.0063 & 0.0078 & 0.1649 & 0.0120 & 0.0019 & 0.6600 & 0.5631 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: PLSR detection results of TSS based on full spectral data with data processing methods. Figure 3: PLSR detection results of TSS based on Savitzky-Golay processed data. The range of MIs was from 0.6911 to 0.7803. In order to eliminate low correlation features to improve the detection ability, we successively deleted the features with corresponding MIs less than 0.70, 0.71, 0.72, 0.73, 0.74, 0.75, 0.76 and 0.77. The remaining features were used for PLRR modeling analysis, to check if the detection ability was better after feature elimination than ability before. The analysis results are shown in Table 3. In this table, the MI range means its corresponding features would be kept for PLRR analysis. The analysis results show that the R\({}^{2}\)cal (R\({}^{2}\) of calibration set) barely changes during the MI larger than or equal to the range of 0.70 to 0.72, slightly decreases during the MI lager than or equal to the range from 0.73 to 0.74, significant decrease during the range of MI lager than 0.74. The R\({}^{2}\)cal (R\({}^{2}\) of validation set) increase gradually during the MI larger than or equal to the range of 0.70 to 0.74 but decrease gradually during the range of MI larger than 0.74. Thus, the optimal features should be extracted while the corresponding MIs larger than or equal to 0.74, and the feature number is decreased from 2151 to 736. Even though the R\({}^{2}\)cal of PLRR detection based on whole feature slightly larger than that based on 736 features, that could be redundant information caused over fitting, since the corresponding R\({}^{2}\)cal increased. The PLRR results of calibration and validation sets based on 736 features of Savitzky-Golay processed data were also shown in Figure 5.  
Figure 4: Mutual information (MI) between TSS and feature of each wavelength. Figure 5: PLRR detection results of TSS based on 736 features of Savitzky-Golay processed data. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**MI Range** & \(\geq\)**0.70** & \(\geq\)**0.71** & \(\geq\)**0.72** & \(\geq\)**0.73** & \(\geq\)**0.74** & \(\geq\)**0.75** & \(\geq\)**0.76** & \(\geq\)**0.77** \\ \hline
**Remaining Feature Number** & 2140 & 1994 & 1635 & 1251 & 736 & 278 & 96 & 15 \\
**R\({}^{2}\)cal** & 0.8983 & 0.8974 & 0.8984 & 0.8675 & 0.8627 & 0.8319 & 0.7866 & 0.3325 \\
**R\({}^{2}\)cal** & 0.6602 & 0.6607 & 0.6620 & 0.6655 & 0.6807 & 0.6769 & 0.4531 & 0.1516 \\ \hline \end{tabular}
\end{table} 
Table 3: PLRR detection results of TSS based on spectral data with MI feature elimination.