## 5 Results
### Knee Valgus Angle
#### 5.2.3 Between-Participant Cross-Validation  
Figure 18 shows the between-participant cross-validation results for three consecutive jumps for participants A, B, C, and E using the RFR and LSVR, and Figure 19 shows the results for participant D. In the analysis of Figures 18 and 19 for each machine learning algorithm, both algorithms sometimes underestimated or overestimated the knee valgus angle compared to the true values, with large deviations. In the analysis of the maximum values of the knee valgus angle estimation results for participant C in Figure 18, the RFR demonstrated a higher estimation accuracy than the LSVR. Thus, for movements that impact the knee joint like jumps, the RFR might be more suitable for estimating knee valgus angles. However, due to the large errors observed in the results for other participants, using the RFR with data from other users might not be effective for estimating knee valgus angles during jumps.  
Finally, Figure 20 shows the between-participant cross-validation results for cutting for participants A, B, C, and E using the RFR and LSVR, and Figure 21 shows the results for participant D. In the analysis of Figures 20 and 21 for each machine learning algorithm, comparing the maximum values of the estimation results for participant E in Figure 20, the RFR less frequently underestimated the knee valgus angle. Thus, for movements with significant knee valgus angle changes like cutting, the RFR might be more suitable for estimating knee valgus angles.  
Based on the validation results of these three movements, when estimating knee valgus angles using data from other users, it is suggested to use the RFR as the machine learning algorithm and to use instantaneous values and the past 20 samples of instantaneous values as features.  
The results from within-participant and between-participant cross-validation for knee valgus angles showed minimal differences in the MAE and RMSE. However, the estimation results from the between-participant cross-validation exhibited large errors across all movements, with noticeable variations in estimation accuracy. Therefore, it is suggested that the proposed method requires using the user's own data for training the model to estimate knee valgus angles accurately. Consequently, for estimating knee valgus angles, it is suggested to use the RFR as the machine learning algorithm and to use instantaneous values and the past 20 samples of instantaneous values from the user's own data.  
From the estimation results of knee flexion angles and knee valgus angles, the evaluation of knee flexion angles in Section 5.1 indicates that it was possible to estimate knee flexion angles using data from other users. However, since estimating knee valgus angles requires the user's own data, it is more accurate for the user if both knee flexion and knee valgus angles are estimated using the user's own data, which also allows for the same burden on the user. Therefore, it is suggested to use the RFR as the machine learning algorithm and to use instantaneous values and the past 20 samples of instantaneous values from the user's own data.  
When purchasing the proposed system, users need to exercise in an environment where stretch sensor values and knee joint angles can be measured for about an hour, similar to this experiment. They should collect their own data, build a machine-learning model using this data, and integrate the model into the system for use.