## 3 Results  
Figure 4 shows the mean triaxial velocities of the 10 feature points used for the analysis. Figure 5 shows the means and standard errors of the correlation coefficients between the observation and prediction of mediolateral and anterior MoS. The values were calculated from the 10 repetitions of cross-validation. Additionally, the figure displays the means and standard errors of the root mean squared errors. For the mediolateral direction, the sacral crest, knee, and shoulder exhibited the greatest correlation coefficients with \(r=0.563\), 0.560, and 0.558, respectively. These three features were followed by C7 and T10, with \(r=0.508\) and 0.489, respectively. The lowest correlation coefficient was recorded at the great trochanter and toe with \(r=0.330\) and 0.250, respectively. The correlation coefficients are significantly different among the 10 feature points (\(F(9,90)=150.4\), \(p<0.001\)). The coefficients of the sacral crest that exhibited the highest value were significantly different from those of the seven features: C7 (\(t(9)=7.11\), \(p=2.52\times 10^{-4}\)), T10 (\(t(9)=4.91\), \(p=3.76\times 10^{-3}\)), elbow (\(t(9)=12.31\), \(p=2.79\times 10^{-6}\)), xiphisternum (\(t(9)=17.12\), \(p=1.60\times 10^{-7}\)), skull (\(t(9)=8.75\), \(p=4.86\times 10^{-5}\)), great trochanter (\(t(9)=14.85\), \(p=5.53\times 10^{-7}\)), and toe (\(t(9)=22.18\), \(p=1.64\times 10^{-8}\)). Figure 4: Mean translational velocities of 10 feature points during a gait cycle. (**a**) Skull, (**b**) T10, (**c**) right shoulder, (**d**) sacral crest, (**e**) xiphistermum, (**f**) C7, (**g**) right elbow, (**h**) right great trochanter, (**i**) right knee, and (**j**) right toe. For the anterior direction, the sacral crest exhibited the highest correlation coefficient between the observation and estimation, with \(r=0.542\). The sacral crest was followed by the shoulder and knee with \(r=0.523\) and \(0.518\), respectively. The lowest coefficient was exhibited by the toe (\(r=0.301\)). The coefficients were significantly different among the \(10\) body features (\(F(9,90)=83.2\), \(p<0.001\)). The correlation coefficient for the sacral crest was significantly greater than those for C7 (\(t(9)=8.57\), \(p=5.72\times 10^{-5}\)), T10 (\(t(9)=7.28\), \(p=2.10\times 10^{-4}\)), elbow (\(t(9)=20.32\), \(p=3.55\times 10^{-8}\)), shoulder (\(t(9)=3.43\), \(p=0.034\)), xiphisternum (\(t(9)=10.97\), \(p=7.41\times 10^{-6}\)), skull (\(t(9)=5.58\), \(p=0.0015\)), great trochanter (\(t(9)=23.68\), \(p<0.001\)), and toe (\(t(9)=18.59\), \(p<0.001\)). Figure 5: Means and standard errors of correlation coefficients and root mean squared errors between estimated and observed MoS values. (**a**) Mediolateral and (**b**) anterior MoS values. *, ** and *** indicate significant difference at \(p<0.05\), \(0.01\), and \(0.001\), respectively, by paired \(t\)-tests with Bonferroni correction of factor nine. Figure 6 shows the MoS values estimated by cross-validation. Each of these two figures includes 300 points, estimated using 10 different models, with 30 points for each. Figure 7 shows the mean triaxial velocities of the sacral crest and the first to third principal motions to estimate the mediolateral MoS. As discussed in Section 2.3, each gait sample is represented as a linear combination of these three principal motions with the principal motion scores (\(\mathbf{t}_{a}\)) indicating the contribution of each motion. Notably, all samples were normalized to have \(\overline{\mathbf{x}}=\mathbf{0}\), and the principal motions highlight the deviations from the mean motions. The estimation of the mediolateral MoS for the sacral crest involves the sum of the three principal motion scores:  
\[\mathbf{m}_{\text{lat}}=0.160\mathbf{t}_{1}+0.0488\mathbf{t}_{2}+0.0457\mathbf{t}_{3}+\overline {m}_{\text{lat}}, \tag{18}\]  
where \(\overline{m}_{\text{lat}}\) is the mean mediolateral MoS value across all samples. As shown in Figure 7b, the characteristic movement of the first principal motion is along the x-axis.