## 5 Experimental Results  
Figure 6 depicts the demonstration results of the baselines and proposed model. In the figure, the closer the points are to the reference line, the better the predictions. All models exhibit an upward trend corresponding to the reference line, demonstrating their effectiveness in food component analysis, though some notable differences exist. When comparing the results of the deep learning-based model in the second column with the traditional machine learning techniques in the first column, the traditional methods are further from the reference line with many predictions significantly deviating. In contrast, the deep learning-based models are relatively closer to the reference line, with a considerable reduction in the number of predictions significantly deviating from the actual values. Table 1 provides a quantitative evaluation for the aforementioned experiment. The traditional machine learning models introduced in [28], such as KNN, LR, DT, RF, and XGB, demonstrated varying performance. The XGB model achieved an \(R^{2}\) of 0.94 and a higher  
Figure 6: Comparison of the prediction results across baselines and the proposed model. The traditional models (KNN, LR, DT, RF, and XGB) show a greater deviation from the reference line, while deep learning models (on the bottom rows) align more closely, indicating superior performance [28; 30; 31]. RMSE of 0.56. On the contrary, the LR model exhibited the lowest \(R^{2}\) value of 0.87 and the highest RMSE of 0.89, indicating the least accuracy among the models evaluated. The deep learning-based model averaged 0.958 for \(R^{2}\), which is higher than the 0.912 for traditional models. Among the models evaluated, the proposed* model achieved the highest \(R^{2}\) value of 0.98. But the CNN, MM, and MM* also demonstrated strong performance with \(R^{2}\) values ranging from 0.94 to 0.96. In addition, the proposed* model showed the lowest RMSE of 0.40, achieving an improvement in RMSE of 5 to 15% over the other deep learning based-models. The results show that incorporating our proposed loss function and rejection metric significantly enhances model performance. Figure 7 illustrates the model's percentage error shown as a boxplot. This visualizes the overall distribution of errors, with extreme errors denoted by the '+' symbol. In evaluating these distributions, a model with short tails is considered effective. All models exhibit an average percentage error close to zero, which reflects good average performance in food nutrient analysis. This observation is corroborated by Table 2, which shows that the average error is close to zero, demonstrating the accuracy of the models. However, a detailed examination reveals significant differences in the error distributions among the models. The tails of the traditional models are generally longer than those of the deep learning models, indicating that traditional models tend to produce more extreme errors. This variability implies that traditional models are less consistent in their predictions. In contrast, the deep learning models show a short tail, meaning that errors occur within a smaller range. This consistency is indicative of the robustness of deep learning models. Among these, the proposed model displays the smallest range of errors, highlighting its precision. Furthermore, the optimized model (proposed*), which includes an autonomous result rejection mechanism, narrows the maximum error range to align closely with the confidence interval of the deep learning model, demonstrating enhanced reliability. \begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline  & **KNN** & **LR** & **DT** & **RF** & **XGB [30]** & **CNN [28]** & **MM [31]** & **MM* [31]** & **Proposed** & **Proposed* \\ \hline \(R^{2}_{adj}\) & 0.93 & 0.87 & 0.90 & 0.92 & 0.94 & 0.95 & 0.94 & 0.96 & 0.96 & 0.98 \\ \hline RMSE & 0.58 & 0.89 & 0.78 & 0.64 & 0.56 & 0.46 & 0.45 & 0.42 & 0.44 & 0.40 \\ \hline \end{tabular}
\end{table} 
Table 1: Comparison results in coefficient of determination (\(R^{2}\)) and RMSE.