# Random Forest-Based Prediction of the Optimal Solid Ink Density in Offset Lithography
## 4 Results  
### Model Training Results  
The trained model can predict the optimal solid ink density for printed materials. Since these target values are discrete, the task can be considered a regression problem. MAE, MSE, RMSE, and R\({}^{2}\) were used as evaluation metrics to assess the model's accuracy. The model parameters were set to the optimized values discussed earlier in the paper and validated.  
After training the model with sample data, the predicted values were compared to the actual data. Figure 7 shows the measured solid ink density values for three different inks (C, M, and Y), compared with the predicted values. As shown in the Figure, the training results of the Random Forest prediction model align well with the actual test results. The prediction model generated by the algorithm after training on a large number of samples, more accurately predicts the solid ink density values for different colors of samples. This verifies that the model has strong generalization ability.  
To further validate the model's training results, the three-color solid ink color block CIELAB L*a*b* values required by the company providing the experimental data were used as input. The model's output density values were recorded, and the optimal solid ink density values determined here were compared to the Chinese national standard GB/T 17934.1-1999 [35]. Additionally, the range of solid ink densities calculated from the validation set was compared with the Chinese national standard GB/T 17934.1-1999. The model's accuracy was assessed based on the degree of approximation of these values, which are presented in Tables 6 and 7.  
The verification results show that the optimal solid ink density values for the three ink colors output by the model fall within the range specified by the GB/T 17934.1-1999 standard. Specifically, the optimal solid ink density for cyan (C) and yellow (Y) inks are within the standard ranges of 1.5 to 2.0 and 0.9 to 1.6, respectively. The optimal solid ink density for magenta (M) ink is 1.61, which aligns with the standard range of 1.3 to 1.6. Furthermore, the calculated density for cyan ink complies with the range set by the Chinese national standards. However, the upper limits of the calculated density ranges for magenta and yellow inks are 1.91 and 1.22, respectively, exceeding the standard values by 0.31 and 0.12.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Printing Ink** & **L*** & **a*** & **b*** \\ \hline C & 56 & \(-35\) & \(-44\) \\ M & 45 & 68 & \(-3\) \\ Y & 83 & \(-5\) & 87 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Standard colorimetric values.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Printing Ink** & **Calculated Density** & **Optimum Solid** & **China’s National** \\  & **Range** & **Ink Density** & **Standard Range** \\ \hline C & 1.57–1.92 & 1.62 & 1.5–2.0 \\ M & 1.56–1.91 & 1.61 & 1.3–1.6 \\ Y & 1.02–1.22 & 1.08 & 0.9–1.1 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Comparison of calculated solid ink densities with standard density values.  
Figure 7: Comparison of predicted and measured solid ink density for CMY three-color inks. (**a**) Comparison of predicted and measured solid ink density of C-color ink. (**b**) Comparison of predicted and measured solid ink density of M-color ink. (**c**) Comparison of predicted and measured solid ink density of Y-color ink.