## 4 Results and Discussion
### Prediction of Human Glucose Concentration
#### 4.2.1 Comparison Analysis of ARD, MARD, and RMSE  
A comparison of the calculated ARD of predicted \(\hat{y}_{i}\) and measured glucose concentrations \(y_{i}\) is shown in Figure 4. Figure 4a-c show the calculated ARD = \(\frac{|y_{i}-\hat{y}_{i}|}{y_{i}}\) of the predicted results made by our HMML-BP network using SNE, diffusion maps, and factor  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & \multicolumn{2}{c}{\(\alpha\)} & \multicolumn{2}{c}{\(\beta\)} & \multicolumn{2}{c}{\(\Delta\)} \\ \cline{2-7}  & \#GData & \#MData & \(\Delta_{1}\) & \(\beta_{\text{GData}}\) & \(\beta_{\text{MData}}\) & \(\Delta_{2}\) \\ \hline SNE & 8.487 & 8.5422 & 0.0552 & 8.4869 & 8.542 & 0.0552 & 0.0001 \\ Diffusion maps & 8.2276 & 8.2604 & 0.0328 & 8.2276 & 8.2606 & 0.033 & 0.0002 \\ Factor analysis & 8.609 & 8.861 & 0.252 & 8.6086 & 8.861 & 0.2524 & 0.0004 \\ \hline \end{tabular}
\end{table}
Table 2: Comparison of similarity \(\alpha\) and difference \(\beta\) of 3D multi-wavelength light data made by SNE, diffusion maps, and factor analysis.  
analysis algorithms. As shown in Figure 4a, those using the SNE algorithm show that samples 9# and 19# are obviously far away from the measured results, the calculated ARD values of which are around 27% and 30%, respectively (Figure 4b). Furthermore, Figure 4c exhibits the prediction results obtained by our network using the diffusion maps algorithm, showing that only sample 19# emerges as obviously different from the measured results, with an ARD of 21% (Figure 4d). The predicted results and ARD achieved by our network using the factor analysis algorithm, as shown in Figure 4e-f, show that all the predicted results are closer to the measured concentrations, with ARD at less than 20%.  
The MARD is calculated to evaluate the predicted accuracy as follows:  
\[\text{MARD}=\frac{1}{n}\times\sum_{i=1}^{n}\left(\frac{|y_{i}-\hat{y_{i}}|}{y_ {i}}\right) \tag{6}\]  
The calculated MARD of the predicted results made by our network using the factor analysis algorithm is 9.98%, displaying the best value in contrast to those achieved using  
Figure 4: (**a**) Predicted results and (**b**) calculated ARD made by the HMML-BP network using the SNE, (**c**) predicted results and (**d**) calculated ARD made using diffusion maps, and (**e**) predicted results and (**f**) calculated ARD made using the factor analysis algorithms.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **MARD** & **RMSE** & **MD** & \multicolumn{3}{c}{**Clark EGA**} \\ \cline{2-6}  & & & & **Region A** & **Region B** \\ \hline SNE & 11.29\% & 0.742 & 0.2445 & 90\% & 10\% \\ Diffusion maps & 10.49\% & 0.787 & 0.1197 & 95\% & 5\% \\ Factor analysis & 9.98\% & 0.789 & \(-\)0.0092 & 100\% & 0 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of blood glucose prediction results from different algorithms.  
the diffusion map and SNE algorithms (10.49% and 11.29%, respectively). Furthermore, the RMSE characterizes the prediction accuracy and is calculated as  
\[\text{RMSE}=\sqrt{\frac{\sum_{i=1}^{n}(y_{i}-\hat{y_{i}})^{2}}{n}} \tag{7}\]  
The calculated RMSE made by our network using the factor analysis algorithm is around 0.742, showing the best performance in contrast to those achieved using diffusion maps and SNE algorithms (0.787 and 0.789, respectively).