## 4 Discussion  
The results listed in Table 1 for \(MV_{AP}\) and \(MV_{ML}\) agree with those of previous studies, indicating that \(MV_{AP}\) is more effective than \(MV_{ML}\) in assessing the postural unsteadiness differences between different age groups and between different health-related conditions [13; 31]. The results listed in Table 2 also demonstrated that the AP-direction tested features were more sensitive in detecting aging effects than the ML-direction tested features were. The best results were obtained by the proposed feature \(\beta_{AP}\) (with a training subset classification accuracy of 0.903 and AUC of 0.954). By comparison, the training subset classification accuracy and AUC achieved by the conventional COP feature \(MV_{AP}\) were 0.739 and 0.777, respectively. Moreover, the classification \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Features**} & \multicolumn{4}{c}{**Classification Accuracy Results**} \\ \cline{2-5}  & \multicolumn{2}{c}{**Training Subsets**} & \multicolumn{2}{c}{**Testing Subsets**} \\ \cline{3-5}  & & \multicolumn{2}{c}{**3-Trial Averaging Samples**} & \multicolumn{2}{c}{**Single-Trial Samples**} \\ \hline  & **Accuracy** & **AUC** & **Accuracy** & **Accuracy** \\ \hline \(\alpha_{ML}\) & 0.576 & 0.504 & 0.563 & 0.548 \\ \(\beta_{ML}\) & 0.606 & 0.589 & 0.590 & 0.583 \\ \(MV_{ML}\) & 0.593 & 0.545 & 0.593 & 0.578 \\ \(\alpha_{AP}\) & 0.818 & 0.886 & 0.810 & 0.727 \\ \(\beta_{AP}\) & 0.903 & 0.954 & 0.895 & 0.839 \\ \(MV_{AP}\) & 0.739 & 0.777 & 0.718 & 0.682 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Classification results of the tested features. accuracy and AUC of the AP-direction features were higher than those of the ML-direction features. Thus, the following discussions focus only on AP-direction features. Note that the results of the discussions can be easily generalized to the ML-direction features. To interpret the results obtained by the proposed features, the remaining part of this section addresses the redundancy problem between \(COP_{y}\) and its GRF components. As shown by Equation (11), there exists an infinite number of combinations of \(F_{yz}\) and \(f_{y}\) for a given \(COP_{y}\). By studying the interactions between these three signals, we attempted to investigate how our balance control system deals with such a redundancy problem. The \(\alpha_{AP}\)-characterized correlation between \(COP_{y}\) and \(F_{yz}\) was high because the mean values of the proposed feature \(\alpha_{AP}\) (0.982 and 0.995 for the younger and older age groups, respectively) were very close to unity (Table 1). By comparison, the \(\beta_{AP}\)-characterized correlation between \(COP_{y}\) and \(f_{y}\) was weaker than that of the correlation between \(COP_{y}\) and \(F_{yz}\) because the values of \(\beta_{AP}\) (0.523 and 0.677 for the younger and older age groups, respectively) were considerably lower than the values of \(\alpha_{AP}\). These results suggested that \(COP_{y}\) is largely determined by \(F_{yz}\). This observation was also evinced by the signal energy of \(F_{yz}\) being much higher than that of \(f_{y}\). In this study, the average value of the energy of the \(F_{yz}\) signal was approximately 1803 times that of the \(f_{y}\) signal. Similar results were also observed in the ML direction. Therefore, we concluded that the COP was largely determined by the vertical GRF components during quiet standing; this finding explained why several previous studies on quiet standing have neglected the contributions of the horizontal GRF components to the COP [45; 46; 47]. Despite the dominant role of \(F_{yz}\) in determining \(COP_{y}\), the following three observations suggested that the influence of \(f_{y}\) is not negligible. First, as indicated in Table 1, the \(\alpha_{AP}\) value of the younger group was significantly lower than that of the older group (\(p=6.62\times 10^{-7}\)).