# Random Forest-Based Prediction of the Optimal Solid Ink Density in Offset Lithography
## 3 Materials and Methods
### Other Machine-Learning Methods for Comparison  
To emphasize the predictive accuracy of the proposed model in determining the optimal solid ink density for printing materials, machine-learning algorithms recognized for their robustness with small sample sizes and low-dimensional datasets were selected for comparative validation, based on the specific characteristics of the dataset used in this study. The selected models included Gradient Boosting (GB), Artificial Neural Network (ANN), Support Vector Regression (SVR), and Polynomial Regression, all trained on the same dataset. Among these, Gradient Boosting (GB) is a robust machine-learning method widely used for regression and classification tasks [30]. It constructs an ensemble predictive  
Figure 5: MSE values for different numbers of decision trees N for CMY tri-color. Figure 6: Comparison of MSE and R2 for different minimum number of nodes in version C. (**a**) MSE values for different numbers of minimum number of nodes. (**b**) R2 for different numbers of minimum number of nodes. model by iteratively adding new learning nodes and enhances prediction accuracy through tunable parameters and various loss functions. Benefiting from its strong nonlinear modeling capability, Gradient Boosting demonstrates excellent generalization performance across different types of datasets, including high-dimensional datasets with numerous features and small datasets. Artificial Neural Networks (ANN) are computational models inspired by biological neural systems, with a core structure comprising synapses, an adder, and an activation function [31]. The connection strength is represented by weights, where positive weights indicate excitatory connections and negative weights indicate inhibitory connections. The adder computes the weighted sum of input signals, while the activation function enables the model to approximate complex functions, generalize patterns, and effectively learn through parameter adjustments. ANN is capable of modeling highly complex nonlinear relationships and is frequently applied in deep learning tasks, particularly excelling in processing large-scale and high-dimensional data. In this experiment, a Multilayer Perceptron (MLP)--a classical feedforward artificial neural network model--was employed for data processing. Polynomial Regression (PR) is an extension of linear regression, commonly used to model nonlinear relationships between dependent and independent variables [32]. By incorporating polynomial terms of independent variables into the model, PR effectively captures nonlinear patterns in data. This model is particularly suitable for applications with small sample datasets, offering low computational cost and requiring minimal computational resources. Support Vector Regression (SVR) is a regression model based on Support Vector Machines (SVM) that constructs a hyperplane in a high-dimensional space to fit the data while minimizing model complexity [33]. SVR is particularly well-suited for applications requiring precise data predictions while preventing overfitting. However, due to its high computational complexity, it is not ideal for large-scale datasets and is highly sensitive to hyperparameter selection. For all machine-learning methods, input parameters were standardized to L*, a*, and b* stimulus values, with model outputs set to solid ink density values. Identical training and validation datasets were used across all tested machine-learning methods. The hyperparameters of the models were optimized using the ten-fold cross-validation method [34]. This method divides the dataset into ten equal subsets, with nine subsets used for training and one for testing in each iteration. The optimized parameter values are presented in the Table 5.