## 3 Methods
### Interaction Embedding Graph
With the addition of predefined target edges and dynamic subject edges, the graph convolution operation also needs to be changed accordingly to complete the representation of the interaction information features, and the improved graph convolution can be expressed as:  
\[ \begin{split}\mathbf{Y}(V_{t}^{i})=\frac{1}{K_{1}}\sum_{k=0}^{k_{ 1}-1}D_{k}^{-1}\phi_{k}(A_{t})\mathbf{X}_{t}\mathbf{W}_{k}+\\ \frac{1}{K_{2}}\sum_{k^{\prime}=1}^{K_{2}-1}D_{k^{\prime}}^{\prime }\phi_{k^{\prime}}^{\prime}(B_{t})\mathbf{X}_{t}\mathbf{W}_{k^{\prime}}\end{split}  \tag{6}\]  
Equation (6) adds a new term to the Equation (2), which completes the modeling of the interaction information. \(K_{2}\) is similar to \(K_{1}\) as a hyperparameter controlling the neighbouring set of each node defined by the subject edge. \(D_{k}^{\prime}\) is the degree matrix of \(\Phi_{k}^{\prime}(B_{t},A_{t})\), which serves to perform normalization of the features by eliminating the influence of the number of neighboring joints on the output, which can be calculated by \([D_{k}^{\prime}]_{ij}=\sum_{j}([\Phi_{k}^{\prime}(B_{t},A_{t})]_{ij})\). \(\mathbf{W}_{k}^{\prime}\in\mathbb{R}^{C\times C^{\prime}}\) is a matrix of learnable parameters formed by superimposing the weight vectors of multiple output channels, where \(C\) and \(C^{\prime}\) represent the input and output feature dimensions, respectively. Similar to the definition of \(\Phi_{k}(A_{t})\), we define \(\phi_{k^{\prime}}^{\prime}(B_{t},A_{t})\) as a polynomial of the adjacency matrix \(B_{t}\) and \(A_{t}\). \[\phi_{k^{\prime}}^{\prime}[k^{\prime}](B_{t},A_{t})= \begin{cases}B_{t},if\ k^{ \prime}=1\\ \mathcal{I}(B_{t}A_{t}^{k^{\prime}-1}-\mathcal{I}(\sum_{i=1}^{k^{\prime}-1} \phi_{i}(B_{t},A_{t})))\end{cases}  \tag{7}\]  
The definition of \(\mathcal{I}(x)\) is the same as its definition in \(\Phi_{k}(A_{t})\). In the neighborhood defined by the joint edges, we use a distance partitioning strategy to partition the neighboring joints into \(K_{1}\) subsets, and use the learnable weights \(\mathbf{W}_{k}\) in each subset to model the influence of the joints in each subset on the central joint to update the features so that it aggregates structural information from the other joints. We also partition the neighboring  
Figure 1: IE-Graph Representation: The joint edge (black) links the joints within the same subject, and the subject edge (red) links the joints of the same kind between different subjects, which models the interactive information. For brevity, we show only a portion of the subject edges in the figure. joints defined by the subject edges into \(K_{2}\) subsets according to the distance partitioning strategy, and model the influence of the joints in each subset on the centroid using the learnable weights \(\mathbf{W}_{k}^{\prime}\), but in this case the graph convolution operation models the interaction information between the subjects. While it is possible to simply increase \(K_{2}\) to make distant joints also neighbors of the central node, there are several drawbacks to such an approach: (1) increased receptive fields increase the model memory and inference time cost; (2) excessively large \(K_{2}\) can result in loops that make the model represent redundant joint dependencies. Therefore, we introduce a data-driven dynamic subject edge. In the implementation, we represent it as a learnable matrix \(B^{\prime}\) with the same dimensions as \(B_{t}\), accompanied by \(B^{\prime}_{t}\) at each occurrence of \(\phi^{\prime}[k^{\prime}](B_{t},A_{t})\) and denoted as \(\phi^{\prime}[k^{\prime}](B_{t},A_{t})+B^{\prime}\). Note that \(B^{\prime}\) is shared in each graph convolution operation and is initialized to an all-zero matrix.