## 4 Methodology  
### Generation of Multi-Agent Graph  
The scene description in Figure 2 illustrates the dynamic structure of vehicles in the intersection at two consecutive time steps. Initially, vehicle1 senses _vehicle3_, and the phase is green with an accessible state. Next, at \(T=2\), vehicle5 enters the perception range of vehicle1 while the phase turns red, resulting in a change in the movement of vehicle1. The processes described above visually elaborate the effects of surrounding vehicles and traffic rules on the target object. Inspired by the agents' mutual topology, we depict these intersections among vehicle-vehicle and vehicle-traffic rules as a self-linkage graph \(G=\{V,\mathcal{E}_{S},\mathcal{E}_{T}\}\). Each vehicle along with traffic rules (traffic signal and stop line) are treated as the node and represented with \(V=\{\
u_{1},\
u_{2},\cdots,\
u_{n}\}\), where \(n\) is the number of nodes. The graph \(G\) edge sets \(E\) are consciously partitioned into spatial \(\mathcal{E}_{S}\) and temporal \(\mathcal{E}_{T}\), of which \(\mathcal{E}_{S}=\{v_{i}^{t}v_{j}^{t}|i,j\in n\}\) and \(\mathcal{E}_{T}=\{v_{i}^{t}v_{i}^{t+1}|i\in n\}\). The \(\mathcal{E}_{S}\) indicates that at each time step, each node is connected to its surrounding nodes within a radius threshold \(D\), which reflects the spatial intersection. The self-connection at the adjacent horizon is denoted by \(\mathcal{E}_{T}\) to learn identity features in the temporal dimension. The graph \(G\) can be expressed mathematically as an adjacency matrix \(\tilde{A}=A+I\) made up of the elements with 0 or 1, where \(\tilde{A}\) can further be displayed in \(\tilde{A}|G=\{V,\mathcal{E}_{S},\mathcal{E}_{T}\}=A|\mathcal{E}_{S}+I| \mathcal{E}_{T}\). In particular, the element \(a\) of matrix \(A\) is defined as (6), representing that when the distance between nodes is less than \(D\), the corresponding edge is connectivity assigned with 1; otherwise, the value is 0.  
\[a_{ij}=\begin{cases}1,&\text{if }\|v_{i}^{t}v_{j}^{t}\|<D\\ 0,&\text{if }\|v_{i}^{t}v_{j}^{t}\|\geq D\end{cases} \tag{6}\]  
It is worth noting that the traffic rules are innovatively introduced into the trajectory anticipation problem in our proposal. However, in the process of fusing trait data from diverse sources, one tricky issue arises: the fact that trajectories of vehicles are spatial-temporal data, whereas traffic-light data are time-series data. The different data characteristics would impose the generated graph transforming to heterogeneous data, arousing a high level of modeling complexity. To simplify the drawback without losing the purpose, we develop an  
Figure 2: Framework of the proposed vehicle trajectory prediction model. The overall architecture contains three portions, namely the generation of multi-agent graph module (GMG), the attention-based spatial–temporal fusion graph module (ASTFG) and the trajectory prediction module (VTP). The attention mechanism (ATT) is introduced to the AST-GCN part, where spatial GCN and temporal GCN are elaborated.  
ingenious solving method, where the signal phase is moved to the intersection stop line and is visualized in 2D space. Only when the phase turns red does the stop line emerge. In such a way, the traffic rules become the same spatial-temporal data as vehicles trajectories, of which the stop line is applied to reflect the spatial position and the temporal attribute is described by signal phase changes. Concentrating the signal phase on the stop line of a lane depends on which direction and lane of traffic the signal light allows to pass, indicating a vehicle's right-of-way. The advantages of the introduced method lie in two respects: one is to prevent the heterogeneous scene, and the other is to integrate the different traffic rules uniformly.