## 3 Results and Discussion
### Optimum Wavelength Selection  
SPA was first used for the selection of the optimal wavelengths for the discrimination of black-heart white radiishes, followed by preprocessing with SNV and mean center. During the SPA selection procedure, the SPA-MLR procedure was used to acquire the RMSE values based on the selected variable subsets. In the toolbox, the maximum number of variables selected by SPA was set as 27, because the number of variables reached 27, the RMSE value was lowest. As shown in Figure 4a, the RMSE values gradually decreased as the number of selected wavelengths increased from 1 to 11. When the number exceeded 10, RMSE did not perceptibly change. Using 10 selected wavelengths for the MLR model (solid square markers), the root mean square error (RMSE) reached its optimal values  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Pretreatment Methods** & **NP** & **SGFD** & **D** & **SGS** & **MSC** & **SNV** & **A** & **MC** & **SNV+MC** \\ \hline LVs & 4 & 4 & 4 & 3 & 3 & 4 & 4 & 8 & 5 \\ Calibration (\%) & 97.5 & 98.1 & 98.1 & 96.6 & 98.1 & 99.1 & 98.1 & 98.8 & 100 \\ Prediction (\%) & 95.6 & 96.1 & 96.7 & 95.6 & 96.7 & 98.9 & 96.7 & 98.3 & 99.4 \\ \hline \hline \end{tabular}
\begin{tabular}{l} LVs: Latent variables; NP: Not preprocessing; SGFD: Savitzky-Golay first derivative; D: Detrend; SGS: Savitzky-Golay smoothing (Width=5); MSC: Multiplicative scatter correction; SNV: Standard normal variate; A: Autoscale; MC: Mean center; SNV: Standard normal variate. \\ \end{tabular}
\end{table}
Table 1: Comparison of the different preprocessing methods based on partial least squares discrimination analysis (PLSDA) models.  
Figure 3: Mean relative transmittance spectra and standard deviation (SD) calculated from the regions of interest (ROIs) of all the normal and defective white radiishes.  
(0.15834) for the two-class discrimination. The selected ten optimal wavelengths designated by open or solid circle markers and their distribution in the typical preprocessed spectral curves are shown in Figure 4b. Figure 4b shows the spectral curves of single normal and black-heart radiishes respectively after preprocessing using SNV+ mean center. In order of importance in the projection procedure, the wavelengths were 642, 629, 655, 730, 611, 809, 724, 738, 545 and 564 nm.  
In order to further reduce the number of input wavelengths, Pearson's linear correlation coefficients and probability levels were analyzed in Table 2. There were very high and positive correlations among the 10 wavelengths with coefficients in the range of 0.843-1.000. Furthermore, the correlations among the groups of 545 nm and 564 nm; 611 nm, 629 nm, 642 nm, and 655 nm; 724 nm, 730 nm, and 738 nm were extremely high with coefficients exceeding 0.990. This cross-correlation indicates that one of the wavelengths in each group can provide the same information as the other wavelengths in the group. Therefore, in line with the importance in the projection procedure in SPA, 642 nm, 730 nm, 809 nm, and 545 nm were selected (designated by open circle markers in Figure 4b) to build the classification model, in which their correlation coefficients were in the range of 0.843-0.987. Models developed using those four wavelengths will be compared with other models based on the ten wavelength inputs and the full wavelengths inputs.