## 3 Materials and Methods
### Assessing Motion Accuracy of Baduanjin  
Before performing the motion assessment, two traditional Chinese sports teachers from a university in Southwest China were invited to give the scores for the motion accuracy. The teachers have more than ten years of experience teaching Baduanjin in the university, and they were required to score each student's motion based on recorded videos. Each motion was scored according to three categories: Fail, Pass and Good. To ensure the consistency of assessment, the Kendall correlation coefficient test was used to calculate the correlation between scores on motion accuracy of students from the two teachers. The results are shown in Table 2.  
Figure 6: The first three features of the eight motions of Baduanjin. From Table 2, we can see that the captured motions of Baduanjin from students have three different levels of motion accuracy, namely Fail, Pass and Good, except for Motion-8, where no student failed in this motion. According to the two teachers, this is because Motion-8 is the simplest motion in Baduanjin and easy to learn (Figure 7). Students can master the essentials of Motion-8 through short-term learning, but long-term practice is needed to achieve high motion accuracy. Moreover, the Kendall coefficient between the scores from the two teachers ranged from 0.824 (Motion-3) to 0.944 (Motion-7). This result indicates that the two teachers have a high degree of consistency in the scores of the students' motion accuracy. On scores of teachers, through the application of 10-fold cross-validation, the effectiveness of different classifiers was trained and verified to assess the motion accuracy. The accuracy of motion assessment of different classifiers, using scores from Teacher A, is shown in Table 3. Using Motion-1 as an example, the confusion matrices for different classifiers for Motion-1, using scores from Teacher A, are shown in Figure 8. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multirow{2}{*}{**Motions**} & \multicolumn{3}{c}{**Teacher A**} & \multicolumn{3}{c}{**Teacher B**} & \multirow{2}{*}{**Kendall**} \\ \cline{2-2} \cline{5-8}  & **Good** & **Pass** & **Fail** & **Good** & **Pass** & **Fail** & **Value** \\ \hline Motion-1 & 16 & 57 & 22 & 15 & 55 & 25 & 0.941 \\ Motion-2 & 21 & 53 & 21 & 24 & 50 & 21 & 0.882 \\ Motion-3 & 26 & 58 & 11 & 23 & 49 & 23 & 0.831 \\ Motion-4 & 22 & 58 & 15 & 19 & 49 & 27 & 0.824 \\ Motion-5 & 20 & 57 & 18 & 20 & 56 & 19 & 0.838 \\ Motion-6 & 23 & 55 & 17 & 20 & 54 & 21 & 0.907 \\ Motion-7 & 29 & 59 & 7 & 26 & 62 & 7 & 0.944 \\ Motion-8 & 61 & 34 & 0 & 61 & 34 & 0 & 0.862 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The grading by two teachers and the Kendall correlation of the scores. Figure 7: Motion-8. Tables 3 and 4 show that, where the scores of Teacher A and Teacher B were used as the supervision for training classifiers, \(k\)-NN has the best accuracy for all types of motions, except for Motion-7. The accuracy for motion assessment on all motions (except Motion-7) is over 86%. However, for assessing the motion accuracy of Motion-7, the results show that SVM has the highest accuracy, reaching 95.79% (for Teacher A) or 87.37% (for Teacher B). It is found from the confusion matrixes that, for the classifiers, \(k\)-NN and SVM, which achieved higher accuracy, the confusion in the assessment of motion accuracy on Motion-1 mainly occurs between Pass and Fail. Besides the accuracy of evaluation, for practical applications, the processing time for each classifier is verified in this study.