# A Study on DNN-Based Practical Model for Predicting Spot Color
## 2 Materials and Methods
### Data Preprocessing  
The data was obtained from operator-recorded measurements, which posed a challenge in ensuring absolute accuracy due to potential recording errors and measurement discrepancies. To obtain reliable results, entries with reflectance values below 0 or above 100, as well as those with zero total ink usage, were removed, resulting in 8267 valid data points out of a total of 19,032. The reason for excluding reflectance values outside the 0-100 range is that reflectance is measured as a percentage. Values below 0 or above 100 indicate likely errors in measurement or data collection, likely due to the challenges associated with delegating data collection to field workers. Such anomalies are not feasible within the standard parameters of reflectance measurement and are treated as inaccuracies. In addition, the removal of records with zero total ink usage is based on the fundamental principle of spot color ink production. Each row in our data set represents a record of spot color ink created by mixing different material inks. When the total amount of material ink used is recorded as zero, it contradicts the very process of ink creation and suggests a recording error or data entry oversight. Therefore, these records were considered invalid for the purposes of our analysis to ensure the integrity and reliability of the data set. In some cases, despite the consistent mixing process, the measured color values show variations (as shown in Table 2). While minor color differences may appear as noise, data points with significant color differences were considered potentially detrimental to the performance of the model. Therefore, a simple algorithm was created to recognize and remove such inaccurate data points prior to model training. The data can be divided into three groups based on the ink used for mixing and its corresponding usage. These groups consist of data sets that share a common mixing method with one data point, two data points, or more than three data points. If there is only one data point for a particular mixing method, the data is considered to be accurately collected. Discrepancies are detected based on color values when the same mixing method appears in multiple data points. However, since print results may vary depending on the \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Features** & **Unit/Range** \\ \hline \multirow{4}{*}{Spot Color} & \(L^{*}\) (luminance) & \([0,100]\) \\  & \(a^{*}\) (green-red coordinate) & \([-128,127]\) \\  & \(b^{*}\) (blue-yellow coordinate) & \([-128,127]\) \\  & Spectral reflectance 1 & \% \\ \hline Basic Ink & Amount used for mixing 2 & mg \\ \hline \multirow{4}{*}{Paper} & Width & mm \\  & Height & mm \\ \cline{1-1}  & Weight & mg \\ \cline{1-1}  & Spectral reflectance 1 & \% \\ \hline \hline \end{tabular} \({}^{\dagger}\) Divided into 31 sections from 400 nm to 710 nm. 2 By 62 inkcodes.  
\end{table} 
Table 1: Collected data on spot color ink manufacturing. test paper used, the anomaly detection process also takes into account the color similarity of the paper. Since the color information of the paper was collected only through the spectral reflectance, the LAB converted value was used. First, if a subset of data sharing a mixing method consists of two entries with a small difference in paper color but a significant difference in printed color, both are considered anomalous (since it's difficult to determine which is correct, both are excluded). If more than three entries are created using the same mixing technique, this subset of data is clustered based on paper color similarity. If a cluster is formed that contains two entries with significant differences in printed color, they are identified as anomalies. For clusters with more than three entries, any data point that has a significant average color difference from the others within the cluster is categorized as an outlier. Here, the color difference is measured in National Bureau of Standards(NBS) units (1), a scale that has perceptual thresholds for values.