## 5 Results
### Knee Flexion Angle
#### 5.1.2 Between-Participant Cross-Validation  
Table 2 shows the mean MAE and RMSE of knee flexion angles for all movements in between-participant cross-validation. Table 2 indicates that both the MAE and RMSE are smaller with Feature A, suggesting that when estimating knee flexion angles using data from other users, it is better to use instantaneous values only.  
To confirm the estimation accuracy of each machine learning algorithm, we compared the knee flexion angle estimation results using instantaneous values only. Figure 10 shows the between-participant cross-validation results for running from all participants using the RFR and LSVR. In an analysis of Figure 10,b, both algorithms showed consistent  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **RFR** & \multicolumn{2}{c}{**LSVR**} \\ \hline  & **Feature A** & **Feature B** & **Feature A** & **Feature B** \\ \hline MAE [\({}^{\circ}\)] & 8.73 & 8.86 & 8.35 & 9.49 \\ RMSE [\({}^{\circ}\)] & 10.84 & 11.06 & 9.93 & 10.86 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Estimation errors of knee flexion angle in between-participant cross-validation.  
Figure 8: Within-participant cross-validation results for three consecutive jumps for participant E.  
Figure 9: Within-participant cross-validation results for cutting for participant D.  
estimations without major deviations. Additionally, when examining the minimum values of the estimation results for participants C and E, the RFR demonstrated a higher accuracy for smaller knee flexion angles. Thus, for movements with significant knee flexion angle changes like running, the RFR is more suitable for estimating knee flexion angles.  
Next, the estimation results from the inter-participant cross-validation of the RFR and LSVR for the triple jump are presented in Figure 11. In the analysis of panels (a) and (b) of Figure 11, neither machine learning algorithm significantly deviated from the estimated values. A comparison of the minimal values in the estimation results for participants A and E, segmented by an algorithm, showed that the RFR had a higher estimation accuracy for smaller knee flexion angles. Therefore, for movements like jumping that impact the knee joints, the RFR is better suited for estimating knee flexion angles.  
Figure 10: Between-participant cross-validation results for running from four participants.  
Figure 11: Between-participant cross-validation results for three consecutive jumps from all participants.  
Figure 12 displays the results from the inter-participant cross-validation of the RFR and LSVR for cutting. In panel (a), the LSVR achieved a better accuracy in estimating smaller knee flexion angles for participant C, while the RFR excels in similar conditions for participant E in panel (b). These findings imply that for actions like cutting, where the knee valgus angle undergoes substantial changes, both machine learning algorithms could be effectively utilized.  
The analysis from these three types of movements indicates that using data from other participants to estimate knee flexion angles tends to yield better results with the RFR, particularly when only instantaneous values are employed as features. While the MAE and RMSE values were higher in inter-participant cross-validation compared to intra-participant, the overall differences in estimation across various movements were minimal.  
The proposed method ideally allows for the estimation of knee joint angles using only data from other individuals, without the need to collect accurate data from the user beforehand. Therefore, using data from other individuals for estimating knee flexion angles is preferable. Based on these results, it is suggested that the proposed system should utilize the RFR algorithm and only instantaneous values from other individuals' data for the estimation of knee flexion angles.  
Figure 12: Between-participant cross-validation results for cutting from all participants.