# A Study on DNN-Based Practical Model for Predicting Spot Color
## 2 Materials and Methods
### Deep Learning Model  
To create a predictive model for spot color inks, we used deep learning techniques. We selected the mixing method of the basic inks and the characteristics of the paper as input features for the model, recognizing their significant influence on the resulting colors. To address problems that may arise from the high dimensionality of the input features, we converted the color and specification information of the paper into LAB values and density, respectively. We also excluded five types of basic inks that were not used in any data. In addition, we simplified the model to directly predict LAB values for better interpretability when analyzing the results. Figure 1 is the result of the correlation analysis on the input features, which shows no obvious spatio-temporal dependencies among the selected input features. Thus, CNN or RNN models proved to be ineffective for learning from this data. Therefore, a Deep Neural Network (DNN) architecture was implemented to effectively process structured data for model design. The designed DNN model consists of a single input layer, several hidden layers, and a single output layer. The input layer is composed of neurons representing 61 input features, while the output layer is composed of three neurons representing the \(L^{\star}\), \(a^{\star}\), and \(b^{\star}\) color values we want to predict (Figure 2). The expressiveness of such a DNN structure is due to the number of hidden layers and the corresponding number of parameters. As the depth of the network increases, it can learn complex data patterns more accurately. However, simply increasing the depth of the network is prone to problems such as gradient vanishing and overfitting. To improve  
Figure 1: Correlation coefficients between the input features. \begin{table}
\begin{tabular}{c c c} \hline \hline
**NBS Unit** & \multicolumn{2}{c}{**Critical Remarks of Color Difference**} \\ \hline
0–0.5 & Trace & Extremely slight change \\
0.5–1.5 & Slight & Slight change \\
1.5–3.0 & Noticeable & Perceivable \\
3.0–6.0 & Appreciable & Marked change \\
6.0–12.0 & Much & Extremely marked change \\
12.0+ & Very much & Change to other color \\ \hline \hline \end{tabular}
\end{table} 
Table 3: NBS ratings [38]. the performance of the model while remaining robust to these challenges, the following strategies were employed in this study. * SELU Activation Function: SELU is a variant of the ELU function. It has self-normalizing property that keeps the output of each layer at a mean of 0 and a standard deviation of 1 during training. This helps to avoid problems such as gradient vanishing or explosion, thereby improving the stability of the learning process [39]. However, these properties are maintained exclusively under certain model structures, namely fully connected layers in feed-forward neural networks. As the DNN structure used in this study adheres to this framework, SELU was chosen as the activation function. Before being fed into the model, the input features are standardized, and all hidden layer weights are initialized using the LeCun initialization technique to employ SELU. * AdamW Optimizer & Early Stopping: The model optimization algorithm used the AdamW optimizer, an improved version of Adam that applies weight decay through L2 regularization. AdamW is known to limit model complexity, thus preventing overfitting to the training data and improving generalization capabilities [40]. In addition, we adopted an early stopping strategy, where model weights are only saved when performance declines on the validation data. This approach aims to mitigate overfitting. * 1-Cycle Scheduling [41]: The learning rate starts at a low initial value during training, then increases rapidly to reach its peak, and finally decreases to a value lower than the initial setting. This approach prevents the model from getting stuck in local optima, allowing for rapid convergence. Once the model has converged, minor adjustments are made to ensure optimal weight exploration.