# Random Forest-Based Prediction of the Optimal Solid Ink Density in Offset Lithography
## 5 Discussion  
The validation results demonstrate that the machine-learning model proposed in this study effectively establishes a quantitative relationship between chromaticity coordinates and ink density values, thereby aiding manufacturers in identifying the optimal solid ink density parameters prior to production. Among all the machine-learning models evaluated, the Random Forest (RF) model achieved superior performance in terms of both accuracy and reliability. Additionally, visual analysis confirmed that the RF model did not exhibit signs of overfitting. These findings underscore the importance of selecting a high-performance model during the calibration stage of the printing process to ensure accurate prediction of optimal solid ink density. During validation with the standard solid ink colorimetric values, slight deviations were observed in the case of magenta ink. However, further analysis indicated that these deviations resulted from differences between the paper and ink used in this study and those prescribed by the Chinese national standards. Paper brightness, smoothness, ink absorption, and viscosity significantly affect color intensity under identical ink density conditions. Experimental measurements indicate that the ink viscosity in this study was 19 Pa-s, whereas the Chinese Light Industry Standard GB/T 2624-2012 [36] (\"Sheet-Fed Offset Printing Ink\") specifies a recommended viscosity range of 10-15 Pa-s. Excessive ink viscosity compromises fluidity, resulting in higher solid density and uneven ink distribution. All regression models successfully achieved density matching. Although Artificial Neural Networks (ANN) and Support Vector Regression (SVR) are popular regression methods and have demonstrated strong performance on many datasets, their regression accuracy on the Lab* colorimetric values dataset was lower than that of polynomial regression and random forest. Experimental results indicate that the regression coefficients for ANN and SVR were only 0.723 and 0.76, respectively, which are suboptimal for practical applications. Due to ANN's high sensitivity to data, it exhibited significant bias in both low- and \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Index**} & \multicolumn{3}{c}{**25C19M19Y**} & \multicolumn{3}{c}{**50C40M40Y**} & \multicolumn{3}{c}{**75C66M66Y**} \\ \cline{2-10}  & **L** & **a** & **b** & **L** & **a** & **b** & **L** & **a** & **b** \\ \hline
1 & 76.1 & 0.1 & \(-\)0.3 & 58.4 & \(-\)0.5 & \(-\)0.7 & 37.6 & \(-\)1.5 & \(-\)0.7 \\
2 & 75.9 & 0.3 & \(-\)0.5 & 57.5 & 0.8 & 0.3 & 36.5 & \(-\)1.8 & \(-\)1.3 \\
3 & 75.3 & 0.5 & \(-\)0.6 & 57.7 & \(-\)0.3 & \(-\)0.2 & 35.7 & \(-\)1.3 & \(-\)1.2 \\
4 & 75.7 & 0.4 & \(-\)0.2 & 58.8 & 0.9 & 0.8 & 36.8 & \(-\)0.9 & 0.8 \\
5 & 76.1 & 0.3 & \(-\)0.4 & 57.9 & 0.8 & \(-\)0.5 & 37.9 & \(-\)1.8 & \(-\)0.5 \\
6 & 75.3 & 0.2 & \(-\)0.3 & 59.4 & 0.6 & \(-\)0.4 & 38.4 & \(-\)1.6 & \(-\)1.4 \\ Average & 75.7 & 0.3 & \(-\)0.3 & 58.2 & 0.3 & \(-\)0.1 & 37.1 & \(-\)0.1 & \(-\)0.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Neutral gray colorimetric values of gray patches composed of CMY combinations. high-density regions [37]. This sensitivity hinders its ability to handle discrete datasets, particularly when the number of data points is limited, thereby reducing prediction accuracy. Additionally, the stochastic nature of small datasets makes ANN training more susceptible to the influence of initial weights, often leading the model to converge to different local optima and resulting in unstable training. While SVR is effective in capturing nonlinear relationships in certain applications, it exhibited higher error values and weaker predictive performance in the dataset used in this study compared to other machine-learning models. SVR relies on well-tuned hyperparameters to achieve optimal generalization. However, in limited datasets, hyperparameter tuning becomes challenging, increasing the risk of underfitting.