# Evaluation of Human Action Based on Feature-Weighted Dynamic Time Warping
## 6 Numerical Experiments
### Action Evaluation  
1. Similarity calculation: The feature matrix DTW algorithm and the FW-DTW algorithm proposed in this paper were applied to healthy people and patients, respectively, and the similarity of their actions was calculated and averaged to compare the differences between the two methods in healthy individuals and patients; the results are shown in Table 4. After a lot of experimental testing, the weighting ratio of the angle features in the action features was set to \(w_{1}=0.2\), and the weighting ratio of the distance features in the action features was set to \(w_{2}=0.8\).  
Figure 11: Angle features of drinking water action in healthy people (**a**) and patients (**b**).  
By comparing the similarity averages in Table 4, it can be found that the FW-DTW algorithm improved the similarity scores of drinking water and combing hair by 0.0003 in healthy individuals and touching the opposite shoulder and touching the back pocket in patients by 0.0017 and 0.0013, respectively. For patients, the similarity scores of drinking water, combing hair, touching the opposite shoulder, and touching the back pocket increased by 0.0821, 0.0614, 0.1019, and 0.2271, respectively. This is because the feature matrix-based algorithm integrates angle and distance features, while the feature weight-based algorithm reduces the error caused by the angle features and thus improves the similarity, proving that the feature weight-based DTW algorithm makes a significant contribution to improving the similarity of actions. Additionally, by comparing the average similarity values for each type of action between healthy individuals and patients, it was found that the similarity between the template actions and those performed by healthy individuals differed by more than 80% from those performed by patients. This indicates that the proposed evaluation method can effectively assess the action quality of individuals with varying health conditions, identifying those with limb disabilities.
2. Achievement score: In rehabilitation action evaluation, for the four actions of drinking water, combing hair, touching the opposite shoulder, and touching the back pocket, we used the FW-DTW algorithm to score the action similarity data of six healthy people and three patients. The action score-similarity comparison table is shown in Table 5.  
Mathematical fitting was used, and we found that the mathematical relationship of score-similarity is a linear relation.  
A polynomial was fitted to the score-similarity, and the results are shown in Figure 13, where the confidence level of the fitted parameters reaches 99%, which can meet the needs of practical applications.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Action**} & \multicolumn{2}{c}{**Feature Matrix DTW**} & \multicolumn{2}{c}{**FW-DTW**} \\ \cline{2-5}  & **Healthy People** & **Patients** & **Healthy People** & **Patients** \\ \hline Drinking water & 0.9993 & 0.0980 & 0.9996 & 0.1801 \\ Combing hair & 0.9994 & 0.1133 & 0.9997 & 0.1747 \\ Touching the opposite shoulder & 0.9968 & 0.1267 & 0.9985 & 0.2286 \\ Touching the back pocket & 0.9978 & 0.2734 & 0.9991 & 0.5005 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Similarity of actions between healthy people and patients.  
Figure 12: Distance features of drinking water action in healthy people (**a**) and patients (**b**).