## 5 Results and Discussion
### Analysis of Misclassification of THA Gaits  
Building upon the results of the previous subsection, the top two most discriminating kinematic parameters, namely the sagittal angles of hip and knee, are further investigated, particularly for subjects with THA gaits. The subject's gait prediction is classified between the three classes as shown in Table 6. For clarity, the subjects have identification numbers, which are tabulated in the table. The subject's identification number, which is not common in both test datasets of the hip and knee sagittal angles, is removed for simplicity. Moreover, there are multiple gait data that are available for each subject, but only a single piece of data is retained that scores above 50% in the softmax layer. Remarkably, there is no cross-prediction between healthy and HOA for the THA gaits. Explicitly, if a gait of the hip sagittal angle is misclassified as healthy, it can either be healthy or THA on the knee sagittal angle prediction, and vice versa. This is also true for HOA gait misclassification.  
To better understand the relationship between the misclassification of the knee and hip sagittal angles, a close inspection of the conditional probabilities is crucial. Both healthy and HOA misclassifications are utilized, and Venn diagrams of the subjects are plotted to show the relationship between the two best performing kinematic parameters.  
Figure 14: Confusion matrix of the FPA front angle.  
First, healthy classifications are analyzed, and the results are shown in Figure 15. As a nomenclature, \(S\mathbb{N}\) in the figure signifies the subject's identification number in the dataset. Interestingly, there are common subjects that were predicted as healthy between the two best performing kinematic parameters. This would increase our confidence in the success of the THA operations in these subjects. Evidently, the hip sagittal angle provides a reliable prediction on the healthy class with \(P_{hea}(knee_{x}|hip_{x})=83.33\%\), while the knee sagittal angle resulted in a conditional probability of \(P_{hea}(hip_{x}|knee_{x})=50\%\). Simply, when a patient's hip sagittal angle is predicted as healthy, there is a better chance that it has returned to a healthy state.  
Next, HOA predictions are analyzed, and the results are plotted in Figure 16. Similar to healthy predictions, there is also a significant number of common subjects that are predicted as HOA. When two best performing kinematic parameters are giving the same HOA results, this should be analyzed by medical diagnostic experts. This could mean a failure in the THA operation. Also, the hip sagittal angle provides a slightly better prediction for the  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{3}{c}{**Hip Sagittal Angle**} & \multicolumn{3}{c}{**Knee Sagittal Angle**} \\
**HEALTHY** & **HOA** & **THA** & **HEALTHY** & **HOA** & **THA** \\ \hline
1 & 36 & 71 & 1 & 36 & 2 \\
51 & 2 & 23 & 73 & 78 & 71 \\
4 & 27 & 42 & 91 & 74 & 23 \\
24 & 31 & 73 & 51 & 27 & 42 \\
16 & 38 & 91 & 4 & 31 & 34 \\
60 & 68 & 78 & 62 & 37 & 82 \\  & & 74 & 17 & 68 & 72 \\  & & 34 & 16 & & 58 \\  & & 82 & 40 & & 75 \\  & & 62 & 60 & & 48 \\  & & 17 & & & 56 \\  & & 58 & & & 67 \\  & & 75 & & & 10 \\  & & 48 & & & 24 \\  & & 56 & & & 38 \\  & & 67 & & & 29 \\  & & 10 & & & 6 \\  & & 40 & & & \\  & & 37 & & & \\  & & 29 & & & \\  & & 6 & & & \\ \hline \hline \end{tabular}
\end{table}
Table 6: Subjects’ common THA gait prediction.  
Figure 15: Healthy prediction of subjects after THA.  
HOA class with \(P_{hoa}(knee_{x}|hip_{x})=66.67\%\), while the knee sagittal angle resulted in a conditional probability of \(P_{hoa}(hip_{x}|knee_{x})=57.14\%\).