# Discrimination of Severity of Alzheimer's Disease with Multiscale Entropy Analysis of EEG Dynamics
## 4 Discussion  
The results above show that using only a few MSE features as the input of LDA provides a high classification performance in differentiating the healthy subjects from the AD patients. For example, with only two MSE scales at 6 and 15, the F1 score is 0.933 in differentiating the HC and AD2 groups using the simple weighted sum model \"\(MSE(\tau=6)-MSE(\tau=15)\)\" to reflect the degree of health, as listed in Equation (9). The model indicates that the weighted sum values, the AD severity indices, of the EEG signals from the healthy subjects are higher than those from the AD ones. This implies that the MSE values of the healthy are higher than those of the AD patients at small scales, while lower \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Case** & **Electrode** & **Scales** & **F1 Score** & **Accuracy** & **Recall** & **Precision** & **Specificity** \\ \hline
3S & F8 & \(\{2,3,12\}\) & 0.854 & 0.797 & 0.976 & 0.759 & 0.933 \\
4S & F7 & \(\{2,5,6,12\}\) & 0.857 & 0.797 & 0.955 & 0.778 & 0.867 \\
5S & F7 & \(\{1,2,4,15,17\}\) & 0.857 & 0.797 & 0.955 & 0.778 & 0.867 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Optimal F1 score and corresponding accuracy, precision, recall, specificity, selected electrode, and scales for each of the 1S-5S cases. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case**Group** & **HC** & **AD1** & **AD2** \\
**N = 15** & **N = 15** & **N = 15** \\ \hline
3S & 0.02 \(\pm\) 0.02 & \(-\)0.03 \(\pm\) 0.04 & \(-\)0.07 \(\pm\) 0.04 \\
4S & 0.28 \(\pm\) 0.04 & 0.24 \(\pm\) 0.06 & \(-\)0.19 \(\pm\) 0.03 \\
5S & 0.03 \(\pm\) 0.08 & \(-\)0.05 \(\pm\) 0.10 & \(-\)0.13 \(\pm\) 0.07 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of MSE-based weighted sum values among the HC, AD1, and AD2 groups. (The values are labeled as mean \(\pm\) SD.) Figure 4: The weighted sum values of the 45 EEG signals recorded from the optimal electrode for the 3S–5S cases. The 15 circle, 15 diamond, and 15 square symbols are from 15 HC, 15 AD1, and 15 AD2 subjects, respectively. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Case** & **Weighted Sum Model** & & & \\ \hline
3S & \(-\) 0.63 \(\cdot\) MSE (\(\tau=2\)) + 0.76 \(\cdot\) MSE (\(\tau=3\)) \(-\) 0.16 \(\cdot\) MSE (\(\tau=12\)) \(-\) 0.06 \\
4S & \(-\) 0.31 \(\cdot\) MSE (\(\tau=2\)) + 0.86 \(\cdot\) MSE (\(\tau=5\)) \(-\) 0.36 \(\cdot\) MSE (\(\tau=6\)) \(-\) 0.21 \(\cdot\) MSE (\(\tau=12\) \(-\) 0.06 \\
5S & \(-\) 0.10 \(\cdot\) MSE (\(\tau=1\)) \(-\) 0.47 \(\cdot\) MSE (\(\tau=2\)) + 0.78 \(\cdot\) MSE (\(\tau=4\)) \(-\) 0.40 \(\cdot\) MSE (\(\tau=15\)) \(-\) 0.05 \(\cdot\) MSE (\(\tau=17\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The weighted sum models for the 3S–5S cases. than those of the AD patients at large scales. The tendency of the results is consistent with those in the previous studies [3; 4; 5; 6]. As to the F1 scores and the related differentiating performances, Table 1 shows that they do not significantly increase from two to five MSE scales for the 19 EEG electrodes, in general. For example, the F1 scores derived from the EEG signals from electrode T4 are 0.938, 0.966, 0.968, and 1.000 under 2 to 5 MSE scales, respectively. Table 4 shows that the significance levels are similar in differentiating the HC and AD1 groups with 2 to 5 scales. Similarly, Figure 4 illustrates that the performances in differentiating the HC, AD1, and AD2 groups do not improved from three to five scales. Indeed, the differentiating performances are high enough using 2 to 3 MSE scales and may not be positively correlated with the number of scales selected [18]. This implies that a simple model is sufficient to reflect the AD severity. Thus, the simple machine learning models in this study provide a basis for designing new simple algorithms to measure the health degree of EEG signals in the future. MSE was first proposed as a measure of complexity, which reflects the ability of a biological system to adapt and function in an ever-changing environment.