## 3 Methods
### Interaction Embedding Graph  
Because graph convolution is used for spatial domain feature extraction, a predefined graph structure for the graph convolution is required, and the traditional graph structure cannot meet the requirements of accurate interaction recognition for modeling interaction information. Since only the coordinates of joints are used as known data in the skeletal data, the interaction between subjects can be understood as a feature representation of the implicit relationship between different subject joints. While graph convolution can model the relationship between joints within a single subject, it can also model interaction information. The problem is that multiple subjects form multiple independently connected graphs, but information cannot be propagated between them, which is why single-subject action recognition methods cannot achieve superior performance in interaction recognition. First we need to construct a graph representation of each subject, which is the same as the traditional skeleton graph representation, except that there are multiple subjects in the scene, and secondly, we introduce another kind of edge to model the interaction information. To distinguish between these two kinds of edges, we call the naturally connected edge within a subject a joint edge--which connects neighboring joints within the same subject--and call the other kind of edge that connects the same joints between different subjects a subject edge. As shown in Figure 1, we use blue and black nodes to represent the joints of the different subjects, and the corresponding colored edges to represent the joint edges within the different subjects. In addition, we use subject edges to connect the skeleton graphs of different subject constructions. For brevity, we do not label all subject edges in the figure. Intuitively, the subject edge converts the independent skeletal graphs composed of multiple subjects into a unified connected graph, which enables modeling of interaction information and feature fusion between multiple subjects after graph convolution; Objectively, the addition of subject edges increases the number of neighbors of each joint, and as mentioned above, the increase of neighbors in the graph convolution means the increase of the receptive field, which means that each joint can not only learn the feature representation within the same subject, but also obtain useful information from other subjects. Because joint edges and subject edges are discriminatively constructed for modeling spatial structure features and interaction features, we use two different adjacency matrices for separate representations. We also use \(A_{t}\in\mathbb{R}^{MN}\) to denote the adjacency matrix composed of joint edges, where \(M\) and \(N\) are the number of subjects and the number of joints per subject, respectively. In general, the joints of each target labeled by the dataset are the same, so \(A_{t}\) is a diagonal matrix consisting of the joint adjacency matrix of each subject. In addition, we use the adjacency matrix \(B_{t}\in\mathbb{R}^{MN}\) to store our predefined subject edges. Another reason we use two matrices for separate representations is that we use two different matrices of learnable parameters in the network to model joint and subject edges separately, one for learning spatial information and the other for interaction information. However, pre-defined subject edges are not sufficient, as they are less helpful for modeling relationships between joints at longer distances. Inspired by the edge-learnable weight matrix in graph convolution, we propose the subject edge-learnable matrix \(B^{\prime}\), which has the same dimension size as \(B_{t}\). Any graph convolution operation performed with a predefined subject edge \(B_{T}\) is accompanied by a \(B^{\prime}\) to learn the relational representation between distant joints.