# Prediction of Oleic Acid Content of Rapeseed Using Hyperspectral Technique
## 3 Result and Discussion
### Estimation Model of Oleic Acid Content  
The above four types of spectral feature MF-\(\lozenge\), SB-\(\lozenge\), TriP-\(\lozenge\), and SPI-\(\lozenge\) are combined as the input layer of BP neural network model, meanwhile the oleic acid content of rapeseed is combined as the output layer. The symbol '\(\lozenge\)' in MF-\(\lozenge\), SB-\(\lozenge\), TriP-\(\lozenge\), and SPI-\(\lozenge\) denotes \(h(0)\) and \(h(1)\), R\({}_{818}\) and DR\({}_{574}\), SDy and SDr, and DSI (\(R_{572}\), \(R_{574}\)) and NDSI (\(R_{575}\), \(R_{576}\)), respectively. According to the number of characteristic parameters in the combination, univariate, bivariate, ternary, and quaternary models are constructed (At most, only one of each type of feature is selected for combination feature). In this manner, 8 univariate combinations, 24 bivariate combinations, 32 ternary combination, and 16 quaternary combinations can be obtained. We then used the \(R^{2}\), RMSE, and RE to evaluate the performance of BP-based neural network model. Since the result of the BP-based algorithm depends on the random initial weight, the modelling process is repeated 100 times and averaged for comparison. Figure 3 shows the average of \(R^{2}\) over all possible combinations for the univariate, bivariate, ternary, and quaternary models. It clearly shows that the \(R^{2}\) increases (meanwhile the error-bar is decreasing) with increasing the number of parameters in the combination feature. Table 5 lists the best model performance of the four corresponding combinations for the training set and testing set, respectively. An interesting finding uncovers that the performance obtained from the multivariate combination is significantly better than that of the univariate. According to the Table 5, the model performance obtained from the ternary combination and quaternary combinations is significantly superior to that of the univariate and slightly better than that of bivariate combination. Figures 4 and 5 show the visual model results for the training set (left panel) and testing set (right panel) by using the ternary combination {MF-\(h(0)\), SB-DR\({}_{574}\), SPI-NDSI(\(R_{575}\), \(R_{576}\))} and quaternary combination {MF-\(h(0)\), SB-DR\({}_{574}\), TriP-SDr, SPI-NDSI (\(R_{575}\), \(R_{576}\))}, respectively. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Min** & **Max** & **Mean** & **STDEV** \\ \hline MF-\(h(0)\) & 1.1976 & 1.8628 & 1.5511 & 0.1269 \\ MF-\(h(1)\) & 1.2306 & 2.0727 & 1.5900 & 0.1993 \\ TriP-SDy & 0.0176 & 0.5693 & 0.2328 & 0.1490 \\ TriP-SDr & 0.3019 & 1.0011 & 0.6179 & 0.1812 \\ SPI-DSI (\(R_{572}\), \(R_{574}\)) & \(-0.0068\) & 0.0118 & 0.0037 & 0.0037 \\ SPI-NDSI (\(R_{575}\), \(R_{576}\)) & \(-0.0012\) & 0.0047 & 0.0021 & 0.0017 \\ SB-R\({}_{818}\) & 0.2867 & 0.8076 & 0.4937 & 0.1308 \\ SB-DR\({}_{574}\) & \(-0.0002\) & 0.0015 & 0.0005 & 0.0004 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The statistics of the eight selected spectral feature. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Correlation Coefficient** \\ \hline MF-\(h(0)\) & 0.7898 ** \\ MF-\(h(1)\) & 0.7442 ** \\ TriP-SDy & 0.7751 ** \\ TriP-SDr & 0.7442 ** \\ SPI-DSI (\(R_{572}\), \(R_{574}\)) & 0.7862 ** \\ SPI-NDSI (\(R_{575}\), \(R_{576}\)) & 0.7950 ** \\ SB-R\({}_{818}\) & 0.7022 ** \\ SB-DR\({}_{574}\) & 0.782 ** \\ \hline \hline \end{tabular}  
* 0.01 significance level.  
\end{table} 
Table 3: The first two parameters with the best correlation in each hyperspectral feature. In addition, as mentioned in Section 3.1, the multifractal feature depicts the global characteristic of the hyperspectral reflectance, which may bring better model performance for predicting rapeseed's oleic acid content. In order to investigate this, we compared the model results obtained between the feature combinations including and excluding the Hurst exponent. Here, we considered the combinations of univariate, bivariate, and ternary cases.