# Random Forest-Based Prediction of the Optimal Solid Ink Density in Offset Lithography
## 4 Results
### Comparative Evaluation of Model Performance  
In this study, MAE, MSE, and RMSE were employed to evaluate model accuracy, where smaller values indicate higher prediction accuracy. The R\({}^{2}\) metric was used to assess model fit, with larger values signifying better fit. Table 8 and Figure 8 present performance comparison data for solid ink density prediction in prints. These results indicate that all machine-learning models demonstrate strong predictive capabilities. The four accuracy metrics (R\({}^{2}\), MSE, RMSE, and MAE) for both training and test sets reveal that the Random Forest model outperforms traditional prediction models for the colorimetric value and density dataset collected in this experiment. The Random Forest model demonstrated superior performance over the comparative models across all key evaluation metrics. Specifically, when compared to the high-performing polynomial regression model, it achieved reductions of 0.00036 in MSE, 0.0082 in RMSE, and 0.0042 in MAE. Relative to the gradient boosting model, the reductions in MSE, RMSE, and MAE were 0.00017, 0.0043, and 0.0047, respectively. These consistently lower error values--particularly the 7.8% to 11.2% reduction in MAE--suggest that the Random Forest model offers improved consistency between predicted and actual measured values. The Gradient Boosting (GB) model also demonstrates strong regression performance. It has an R\({}^{2}\) value only 0.018 lower than the Random Forest model, an MSE of 0.00046, an MAE of 0.0178, and an RMSE of 0.0216. The Polynomial regression model also performs well, with an MSE of 0.00065, an RMSE of 0.0255, an MAE of 0.0173, and an R\({}^{2}\) of 0.0933. However, its capacity to handle solid ink density is somewhat limited compared to the previous two models. In contrast, the ANN and SVR models exhibit significantly lower accuracy, with R\({}^{2}\) values of 0.7605 and 0.7233, respectively. Their error metrics are notably higher than those of the other models. Conversely, the accuracy of the Random Forest model is superior to that of both ANN and SVR models. Its R\({}^{2}\) value is 0.246 higher than the SVR model and 0.036 higher than the polynomial regression model, indicating superior fit. The effectiveness of the machine-learning models in solid ink density prediction is illustrated in Figure 9. A closer alignment of the predicted value curve with the target true value curve indicates better predictive performance. Among the models, Random Forest, Polynomial Regression, and Gradient Boosting exhibit a closer fit to the true value curve, with smaller deviation values, demonstrating higher accuracy and precision. To improve the accuracy of quantitative evaluation, the discrepancies between the predicted and actual values for each ink color in the validation set were visualized. Figure 10 presents the error statistics of the optimal solid ink density prediction model for cyan ink. As illustrated in the figure, the SVR model exhibited the widest prediction error range, with a maximum error of 1.16 \(\times\) 10\({}^{-1}\) and a minimum error of 1 \(\times\) 10\({}^{-3}\). Similarly, the ANN model yielded a maximum prediction error of 8.9 \(\times\) 10\({}^{-2}\) and a minimum of 4 \(\times\) 10\({}^{-3}\). The PR and GB models demonstrated improved accuracy over SVR and ANN, with maximum errors of 6.3 \(\times\) 10\({}^{-2}\) and 4.9 \(\times\) 10\({}^{-2}\), respectively. The RF model showed the smallest prediction error range, with a maximum error of 4.3 \(\times\) 10\({}^{-2}\) and a minimum of 0. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **MSE** & **RMSE** & **R\({}^{2}\)** & **MAE** \\ \hline Random Forest & 0.00029 & 0.0173 & 0.9692 & 0.0131 \\ SVR & 0.00269 & 0.0518 & 0.7233 & 0.0448 \\ Polynomial & 0.00065 & 0.0255 & 0.9332 & 0.0173 \\ Regression & 0.0023 & 0.0483 & 0.7605 & 0.0401 \\ ANN & 0.00046 & 0.0216 & 0.9513 & 0.0178 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Model metrics after different model training.