## 2 Materials and Methods  
### Human Skeleton Model for Abnormal Gait Recognition  
The human skeleton reflects the important features of body motions. The coordinates of the main joints can be effectively extracted with a depth sensor, as in the Kinect system. The classification accuracy of human behaviors improves as more joints are recognized. As for the abnormal gait recognition, more attention should be paid to the motion of lower limbs. Since pathological gaits may often manifest with abnormal bending of the legs, the body joints extracted by the depth sensor must be winnowed to some extent to improve the feature extraction of limb joints and enhance the efficiency of the training process.  
As shown in Figure 1, the Kinect V2 can acquire the coordinates of 25 body joints, including 8 joints of the hands; Azure Kinect DK can acquire the coordinates of 32 body joints, including 8 joints of the hands and 6 of the head. In abnormal gait recognition, adding this many joints on the hands and head does not substantially help. Thus, the 8 hand joints were simplified as a single center-of-mass key point for each of the left and right hands, and the 6 head joints were simplified to a single key point. The coordinates of each key point are the mean coordinates of the joints on that side of the body.  
\[\begin{split} ComHand_{x,y,z}&=\frac{\Sigma\,I_{x,y,z}}{4},\\ ComHead_{x,y,z}&=\frac{\Sigma\,I_{x,y,z}}{5}, \end{split} \tag{1}\]  
where \(ComHand_{x,y,z}\) is the \(x,y,\) and \(z\) three-dimensional space coordinates of the center-of-mass key point for the hand, and \(\ ComHead_{x,y,z}\) is the \(x,y,\) and \(z\) three-dimensional space coordinates of the center-of-mass key point for the head; these new keypoints are shown as red dots in Figure 1. \(I_{x,y,z}\) is the \(x,y,\) and \(z\) three-dimensional space coordinates of the joint in the corresponding part, as shown by the yellow dots in Figure 1.  
Thus, any human skeleton graph can be represented as \(G=\{V,E\}\), where \(V\) is the set of joints in the streamlined skeleton, and \(E\) is the set of edges corresponding to the physical connections between the joints. For any spatial-temporal series \(T=\{1,2,\ldots M\}\), the corresponding spatial-temporal graph of the skeleton can be represented as \(STG=\{G^{t}|t\in[1,2,\ldots M]\}\), where \(M\) is the number of consecutive frames of the skeleton series, and \(G^{t}\) is the corresponding skeleton graph at time \(t\).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Year** & **Number of Streams** & **Description** \\ \hline \multirow{3}{*}{ST-GCN [18]} & \multirow{3}{*}{2018} & \multirow{3}{*}{1 s} & Firstly constructed a spatial–temporal graph. The parameters of each layer & \\  & & & & are fixed. \\ \cline{4-5}  & & & & Added adaptive graph convolutional layers. The network has a large amount of calculation. \\ \cline{4-5}  & & & & Proposed non-local shift graph \\ \cline{4-5}  & & & & convolution. High computational complexity due to shift operations. \\ \cline{4-5}  & & & & Redefined the k-order adjacency matrix. \\ \cline{4-5} MS-G3D [22] & 2020 & 2 s & Designed a unified spatio-temporal graph convolution operator. \\ \cline{4-5}  & & & & Improved a residual GCN with bottleneck structure and part-wise attention module. \\ \cline{4-5} MST-GCN [20] & 2021 & 4 s & Proposed a multi-scale spatial and temporal graph convolution module. \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of Existing GCN Models.