## 3 Results
### Impact of Different Preprocessing Methods on Data and Model Accuracy
#### 3.2.2 Impact of Different Preprocessing Methods on Model Accuracy  
By comparing the heatmaps, it was found that the preprocessing methods for the four mathematical transformations 1 DR, 2 DR, (LogR)', and (1/R)' were superior. Next, we will compare the modeling results of these four mathematical transformations under different denoising methods. This study employs two machine learning methods, SVM and PLSR, and two deep learning methods, BP and CNN, for modeling. The modeling results are shown in Table 4.  
Figure 6: Heat map of Pearson correlation coefficient under different pretreatment methods. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Preprocessing Methods**} & \multirow{2}{*}{ \begin{tabular}{c} **Modeling** \\ **Methods** \\ \end{tabular}  } & \multicolumn{6}{c}{**Validation Set**} \\ \cline{3-10}  & & **RMSE** & **R2** & **MAE** & **MAE** & **MBE** & **RPIQ** \\ \hline \multirow{8}{*}{1 DR} & SVM & 5.247 & 0.790 & 4.167 & 0.182 & 1.035 & 3.904 \\  & PLSR & 5.768 & 0.746 & 4.938 & 0.215 & 0.247 & 4.035 \\  & BP & 5.991 & 0.726 & 4.779 & 0.211 & 0.786 & 4.514 \\  & CNN & 5.736 & 0.749 & 4.633 & 0.221 & 1.103 & 5.338 \\ \hline \multirow{8}{*}{N-N-} & SVM & 6.427 & 0.685 & 4.948 & 0.216 & 1.918 & 5.203 \\  & PLSR & 6.670 & 0.661 & 5.541 & 0.263 & 1.412 & 4.069 \\  & BP & 7.052 & 0.621 & 5.628 & 0.279 & 1.936 & 5.161 \\  & CNN & 6.286 & 0.699 & 4.983 & 0.236 & 1.181 & 4.647 \\ \hline \multirow{8}{*}{\(\mathrm{(LogR)^{\prime}}\)} & SVM & 4.426 & 0.851 & 3.535 & 0.172 & 1.558 & 3.866 \\  & PLSR & 4.490 & 0.846 & 3.644 & 0.174 & 1.095 & 3.034 \\  & BP & 5.575 & 0.747 & 4.637 & 0.205 & 1.678 & 4.318 \\  & CNN & 5.652 & 0.756 & 4.745 & 0.235 & 2.215 & 3.782 \\ \hline \multirow{8}{*}{\(\mathrm{(1/R)^{\prime}}\)} & SVM & 4.281 & 0.860 & 3.448 & 0.159 & 0.613 & 3.290 \\  & PLSR & 4.181 & 0.867 & 3.467 & 0.151 & 0.580 & 3.719 \\  & BP & 5.860 & 0.738 & 4.535 & 0.233 & 1.809 & 3.831 \\  & CNN & 5.791 & 0.744 & 4.609 & 0.214 & 0.890 & 5.210 \\ \hline \multirow{8}{*}{\(\mathrm{1 DR}\)} & SVM & 5.165 & 0.797 & 4.161 & 0.183 & 0.469 & 4.255 \\  & PLSR & 6.221 & 0.705 & 5.080 & 0.268 & 0.354 & 3.478 \\  & BP & 4.471 & 0.848 & 3.574 & 0.159 & 0.130 & 2.401 \\  & CNN & 5.191 & 0.794 & 4.096 & 0.195 & 0.447 & 3.697 \\ \hline \multirow{8}{*}{\(\mathrm{2 DR}\)} & SVM & 4.100 & 0.809 & 4.135 & 0.190 & 0.832 & 4.583 \\  & PLSR & 5.472 & 0.772 & 4.408 & 0.226 & 0.488 & 3.617 \\  & BP & 5.887 & 0.736 & 4.946 & 0.226 & 0.637 & 4.804 \\  & CNN & 5.779 & 0.745 & 4.848 & 0.245 & 1.049 & 3.384 \\ \hline \multirow{8}{*}{\(\mathrm{SG}\)-S-} & SVM & 4.800 & 0.825 & 4.000 & 0.192 & 1.149 & 4.284 \\  & PLSR & 6.485 & 0.679 & 5.316 & 0.271 & 1.259 & 5.709 \\  & BP & 5.693 & 0.753 & 4.302 & 0.190 & 0.451 & 3.708 \\  & CNN & 5.482 & 0.771 & 4.449 & 0.202 & 1.540 & 4.598 \\ \hline \multirow{8}{*}{\(\mathrm{(1/R)^{\prime}}\)} & SVM & 4.745 & 0.828 & 3.729 & 0.172 & 0.480 & 4.620 \\  & PLSR & 5.447 & 0.774 & 4.439 & 0.210 & 0.535 & 3.199 \\  & BP & 4.887 & 0.818 & 3.826 & 0.183 & 1.154 & 3.790 \\  & CNN & 5.578 & 0.763 & 4.096 & 0.195 & 1.236 & 4.615 \\ \hline \multirow{8}{*}{\(\mathrm{1 DR}\)} & SVM & 5.034 & 0.806 & 3.945 & 0.170 & 0.444 & 4.310 \\  & PLSR & 5.834 & 0.740 & 4.445 & 0.242 & 0.565 & 5.071 \\  & BP & 5.290 & 0.787 & 4.187 & 0.215 & 1.407 & 4.475 \\  & CNN & 5.396 & 0.778 & 4.468 & 0.222 & 1.595 & 4.246 \\ \hline \multirow{8}{*}{\(\mathrm{2 DR}\)} & SVM & 5.365 & 0.780 & 4.169 & 0.184 & 1.407 & 5.302 \\  & PLSR & 6.618 & 0.666 & 5.371 & 0.293 & 1.379 & 4.121 \\  & BP & 6.327 & 0.695 & 4.894 & 0.240 & 2.949 & 4.638 \\  & CNN & 6.197 & 0.707 & 5.158 & 0.241 & 2.96 Among the 16 combinations of four mathematical transformations and four modeling methods, the combinations with SG denoising outperformed the other two denoising methods in several metrics: RMSE was lower in 9 out of 16 cases, R\({}^{2}\) was higher in 10 out of 16 cases, MAE was lower in 8 out of 16 cases, MAE was lower in 8 out of 16 cases, MBE was closer to 0 in 9 out of 16 cases, and RPIQ was lower in 10 out of 16 cases.