## 1 Node attention module  
As shown in Figure 5, the current status of the target node at a certain time is marked as \(h_{j}^{dst}\), for its multiple adjacent nodes, its status is marked as \(h_{i}^{src}\), where \(i=1,2,\ldots,N^{src}\) represents one of all adjacent nodes of node \(j\), and the state of the target node at the next time is affected by the state of all adjacent nodes at the current time.  
\[\alpha_{ij}=A^{node}\Big{(}W^{src}\mathrm{h}_{i}^{src}\parallel W^{dst} \mathrm{h}_{j}^{dst}\Big{)} \tag{24}\]  
The node focus module maps the source node state and the target node state to the same space through the linear layer weights \(W^{src}\) and \(W^{dst}\), respectively. After the splicing operation, the initial node weight \(o_{ij}\) is calculated through the full connection layer weight \(W^{natt}\), and then after the normalization and activation operation.  
\[o_{ij}=\mathrm{LeakyReLU}\Big{(}W^{natt}\Big{(}W^{src}\mathrm{h}_{i}^{src} \parallel W^{dst}\mathrm{h}_{j}^{dst}\Big{)}\Big{)} \tag{25}\]  
\[\alpha_{ij}=\mathrm{softmax}\big{(}o_{ij}\big{)}=\frac{e^{o_{ij}}}{\sum_{j=1 }^{N^{src}}e^{o_{ij}}} \tag{26}\]  
Figure 4: Schematic diagram of attention-heterography module.  
Figure 5: Schematic diagram of node attention module.  
Obtain the final node weight \(\alpha_{ij}\). As shown in Equation (27), the single relationship state variable \(\mathrm{h}_{r}^{rel}\) temporarily records the impact of all adjacent nodes on the state transition of the target node in the relationship \(r\):  
\[h_{r}^{rel}=\overset{i=1}{\oplus}\left(\alpha_{ij}\odot h_{i}^{src^{\prime}}\right) \tag{27}\]  
where \(\oplus\) represents corresponding element addition operation, and \(\odot\) a represents Hadamard product operation.  
2. Relational attention module  
In the heterogeneous graph iteration module, there are usually multiple relationships between nodes, and the relationship attention weight is an important basis on which to measure the impact of different relationships on node status. As shown in Figure 6 below, in a single relationship, the impact of multiple nodes on the state of the target node is weighted by the node attention module and recorded as \(h_{r}^{rel}\). The relational attention module processes the information incentives from all relationships at the current moment through the splicing operation and the linear layer, so as to obtain the weight of different relational signals \(\beta_{j}\).  
\[\beta_{j}=A^{rel}\left(\left\|\mathrm{h}_{r=1}^{rel}\mathrm{h}_{r}^{rel}\right) \tag{28}\]  
As shown in Formula (29), the initial relationship weight \(\mathrm{o}_{j}\) is obtained after initial linear change (\(W^{rel}\)), activation processing (\(tan\)\(h\)), and linear weighting operation (\(W^{ratt}\)).  
\[o_{j}=\left(W^{ratt}\left(\mathrm{tanh}\left(W^{rel}\left(\left\|\mathrm{h}_{ r=1}^{rel}\mathrm{h}_{r}^{rel}\right)\right)\right)\right) \tag{29}\]  
As shown in Formula (30), the final relational attention weight is obtained after softmax normalization \(\beta_{j}=\left(\beta_{1j},\beta_{2j},\ldots,\beta_{N^{rel}j}\right)\).  
\[\beta_{rj}=\mathrm{softmax}\big{(}o_{rj}\big{)}=\frac{e^{\rho_{ij}}}{\sum_{r= 1}^{N^{rel}}e^{\rho_{ij}}} \tag{30}\]  
3. Among these, \(\beta_{rj}\) represents the weight of the r-th relationship to node \(j\).  
In order to further improve the stability of the node attention module, this paper adopts the multi-dimension attention mechanism (MHAM):  
\[H_{tensor}=\left[\mathrm{h}_{1},\mathrm{h}_{2},\cdots,\mathrm{h}_{K}\right] \tag{31}\]  
that is, through multiple attention modules to carry out weighting operations, splice the features from multiple weighted processing to obtain the output results, and help the prediction model achieve better prediction results in the test set:  
\[S_{1}=S_{1\_node}\oplus S_{1\_relationship} \tag{32}\]  
Figure 6: Schematic diagram of Relational attention module.