# Prediction of Oleic Acid Content of Rapeseed Using Hyperspectral Technique
## 3 Result and Discussion
### Estimation Model of Oleic Acid Content
For example, for the bivariate combination, there are 12 combinations including MF parameters (\(h(0)\) and \(h(1)\)) and other 12 combinations exclude them. The averaged  
Figure 4: Model results obtained from the ternary combination {MF-\(h(0)\), SB-DR\({}_{574}\), SPI-NDSI(\(R_{575}\), \(R_{576}\))}. (**a**) is for the 64 training samples. (**b**) is for the 16 testing samples. Figure 3: Average of \(R^{2}\) for the combinations containing different variables. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{3}{c}{**TRAIN (N = 64)**} & \multicolumn{3}{c}{**TEST (N = 16)**} \\ \cline{2-7}  & \(R^{2}\) & **RMSE** & **RE (\%)** & \(R^{2}\) & **RMSE** & **RE (\%)** \\ \hline \(\text{[SPI-NDSI}(R_{575},R_{576})]\) & 0.7777 & 1.3647 & 1.377 & 0.6799 & 1.55 & 1.728 \\ \(\text{[MF-}h(0),\text{SB-DR}_{574}]\) & 0.8635 & 1.0603 & 1.128 & 0.7971 & 1.3388 & 1.678 \\ \(\text{[MF-}h(0),\text{SB-DR}_{574}]\) & 0.8753 & 1.0301 & 1.047 & 0.8169 & 1.2922 & 1.497 \\ \(\text{[MF-}h(0),\text{SB-DR}_{574},\text{TriP-SDr},\) & 0.8652 & 1.0486 & 1.085 & 0.8012 & 1.2706 & 1.526 \\ \(\text{SPI-NDSI}(R_{575},R_{576})]\) & 0.8652 & 1.0486 & 1.085 & 0.8012 & 1.2706 & 1.526 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The best model of different parameter combinations. results over the all-possible combinations are listed in Table 6. It can be observed from the results that the Hurst exponent is not as good as the traditional spectral parameters when the univariate is considered as the argument. However, the Hurst exponent exhibits its superiority in the case of the multivariate model because it brings a significantly better model performance. This finding suggests that the multifractal feature should be an important supplement to the traditional spectral characteristics when we construct the rapeseed's oleic acid content evaluation model. As the last important task, the model test will show the model stability. In order to perform this, we test the model by changing the number of training samples. According to the parameter combinations listed in Table 5, 48-72 samples are randomly selected as the training set, the three evaluators of \(R^{2}\), RMSE, and RE are calculated and shown in Figure 6. It is clearly shown that there is non-significant change of the three indicators with the increasing training numbers, which implies that the selected feature combination brings stable model result. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**MF-**} & \multicolumn{3}{c}{**Training Set (N = 64)**} & \multicolumn{3}{c}{**Testing Set (N = 16)**} \\ \cline{3-8}  & **Features** & \(R^{2}\) & **RMSE** & **RE (\%)** & \(R^{2}\)** & **RMSE** & **RE (\%)** \\ \hline \multirow{3}{*}{Univariate} & with & 0.6232 & 1.748 & 1.913 & 0.6043 & 1.8096 & 2.154 \\  & without & 0.6789 & 1.6399 & 1.752 & 0.6201 & 1.8153 & 2.086 \\ \cline{1-1}  & with & 0.7835 & 1.3451 & 1.432 & 0.7152 & 1.5610 & 1.816 \\ \cline{1-1}  & without & 0.7122 & 1.5326 & 1.634 & 0.6421 & 1.7567 & 2.274 \\ \cline{1-1}  & with & 0.8086 & 1.2498 & 1.353 & 0.7573 & 1.4679 & 1.685 \\ \cline{1-1}  & without & 0.7394 & 1.4754 & 1.601 & 0.6685 & 1.6988 & 1.983 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The influence of MF parameters on model accuracy. Figure 5: Model results obtained from the quaternary combination {MF-_h_(0), SB-DR\({}_{574}\), TriP-SDr, SPI-NDSI(\(R_{575}\), \(R_{576}\))}. (**a**) is for the 64 training samples. (**b**) is for the 16 testing samples.