# Deep Spatio-Temporal Graph Attention Network for Street-Level 110 Call Incident Prediction
## 4 Problem Statement
### Graph Representation  
Consider a graph \(G=(V,\,E,\,X,\,\,\text{A})\), where \(V\) represents the nodes in the graph, \(E\) represents the edges connecting the nodes, \(X\) denotes the node features, and \(\text{A}\) is the adjacency matrix. An adjacency matrix is a mathematical representation of a graph where each row and column corresponds to a node (or street), and the entries indicate whether pairs of nodes are adjacent (connected) in the graph. In our study, the adjacency matrix represents the connectivity between street segments in the urban road network. If \(\text{A}_{ij}=1\), nodes \(v_{i}\) and \(v_{j}\) are adjacent; otherwise, they are not. When applying graph methods to represent street networks, two common approaches are often used.  
The first is the primary graph, where \(V\) represents intersections and \(E\) represents the streets connecting them. This method is advantageous as it accounts for the heterogeneous characteristics of both intersections and streets.  
The second approach is the dual graph [46], which is the inverse of the primary graph: \(V\) represents streets, and \(E\) represents the intersections connecting those streets. A dual graph is a graph that represents the relationships between the edges (streets) of the original graph rather than the nodes (intersections). In this context, each node in the dual graph corresponds to a street segment, and the edges between the nodes represent the adjacency, or connectivity, between street segments. This method emphasizes the properties of the streets and the topological features of the entire network, aligning more closely with the objectives of our research. Consequently, we opted for the dual graph approach.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Factorization** & **Name** & **Content** & **Dimension** \\ \hline \multirow{8}{*}{Spatial features} & Street attribute & one-way; layer; bridge; & \\  & & tunnel; type; length & 6 \\ \cline{2-4}  & Population & population/den & 2 \\ \cline{2-4}  & & dining/den; scenery/den; & \\  & & facility/den; enterprise/den; & \\  & & shopping/den; transportation/den; & \\  & POIs & finance/den; education/den; & 28 \\  & & residence/den; service/den; & \\  & & sports/den; medical/den; & \\  & & government/den; underground/den & \\ \hline \hline \multirow{2}{*}{Temporal features} & \multirow{2}{*}{Calendar} & month; day; weekday; & \\  & & is\_holiday; hour & 5 \\ \hline \multirow{2}{*}{External features} & \multirow{2}{*}{Weather} & wind\_speed; temperature; & \\  & & atmospheric\_pressure; humidity; & \\ \cline{1-1}  & & precipitation & \\ \hline \hline \end{tabular} Note: To enhance the dimensionality of the dataset, we normalized the count values by dividing them by the length of the streets, thus introducing a feature called “density” (den), which represents the value of the feature per unit length of the street. To verify the correlation between the aforementioned spatio-temporal features and the risk of \(110\) Call incidents, we employed binary logistic regression and probabilistic regression methods. The results demonstrate that the vast majority of features are significantly associated with the risk. Detailed verification results are provided in Appendix A.  
\end{table}
Table 1: Spatio-temporal features list.  
Figure 5 illustrates the operational process of this method: panel (a) shows a simplified real-world street network, while panel (b) displays the transformed network produced by this approach. In the transformed network, the red node \(v_{6}\) represents the target street, with the adjacent nodes corresponding to neighboring streets, numbered 2, 3, 8, and 9, respectively.  
Accordingly, utilizing the dual graph method, we constructed a graph \(G=(V,\) X, A), where \(V\) denotes all the streets within our study area. \(X\in\mathbb{R}^{|V|\times M}\) encapsulates the spatial features of these streets, with \(|V|=9654\) and \(M=36\). A is the adjacency matrix of the streets, indicating whether a pair of nodes (streets) intersect with one another.