## 4 Local-Global Dynamic Multi-Graph Convolutional Neural Network Model
### Local-Global Dynamic Spatiotemporal Graph Convolution
#### 4.1.1 Dynamic Multi-Graph Generation Module  
The efficacy of Multi-Graph Convolutional Network (MGCN) models in leveraging diverse semantic information of nodes has been substantiated in the context of shared bicycle traffic prediction [19]. Consequently, inspired by the construction of multiple graphs in MGCN models, we extend this approach to the establishment of dynamic multiple graphs.  
1. Multi-Graph Construction  
The multi-graph construction module involves building three graphs: the distance graph \(G_{dis}\), the historical contact graph \(G_{nis}\), and the POI similarity graph \(G_{poi}\). All three graphs have stations as nodes, and the edges represent connections between stations. The key difference lies in the calculation of adjacency matrix weights, explained as follows:  
* Distance Graph \(G_{dis}\) Incorporating local positional semantic information, the calculation formula is given by Equation (3): \[a_{dis}(i,j)=\left\{\begin{array}{l}\frac{1}{Dis(i,j)},\ Dis(i,j)\leq d\\ 0,\ others\end{array}\right.\] (3) where \(a_{dis}\) represents the weight value of the adjacency matrix \(A_{dis}\) for the distance graph, \(Dis(i,j)\) denotes the straight-line distance between stations, and \(d\) is the set distance threshold. In most cases, bike-sharing stations with closer distances exhibit more similar demands. As the calculation formula for the distance graph follows a threshold structure, with a weight value of 0 for the adjacency matrix when the distance between two stations is beyond the threshold (\(Dis(i,j)>d\)), the graph constructed based on historical ride records captures the correlation features of nearby stations.
* Historical Connectivity Graph \(G_{nis}\) The adjacency matrix of the historical connectivity graph \(A_{nis}\) is computed based on historical ride records, as per Equation (4): \[a_{nis}(i,j)=\sum\
olimits_{start}^{t_{end}}|\{R(SS,\ ES,\ ST,\ ET)|SS=i\wedge ES=j\}|\] (4) where \(a_{nis}(i,j)\) denotes the number of bike-sharing ride records from station \(i\) to station \(j\). \(G_{nis}\) encompasses global positional semantic information. In \(G_{nis}\), nodes with larger edge weights often indicate diverse functionalities between the corresponding two nodes. For instance, frequent records might exist between residential areas and office buildings duringpeople's commuting. Thus, the graph established based on historical ride records captures the close relationship between distant stations at a global level.
* POI Similarity Graph \(G_{poi}\)  
The POI difference graph \(G_{poi}\) includes global positional semantic information and is calculated using the TF-IDF method [41] for the similarity of POIs between stations, as shown in Equation (5):  
\[a_{poi}(i,j)=\frac{TF\_IDF_{i}\cdot TF\_IDF_{j}}{\|TF\_IDF_{i}\|\|TF\_IDF_{j}\|} \tag{5}\]  
where \(\cdot\) denotes the dot product of vectors, and \(\|\;\|\) represents the magnitude of a vector.  
In \(G_{poi}\), larger edge weights indicate higher POI similarity between nodes, signifying that stations with similar functional attributes have similar demand patterns. Thus, the graph established based on POI similarity captures the similarity of demand patterns across stations on a global scale. Although both graphs incorporate global positional semantic information, the distinction lies in \(G_{poi}\), where larger edge weights indicate nodes with similar or identical functional attributes.  
2. Dynamic Multi-Graph Generation  
At each time step, stations undergo dynamic changes. As illustrated in Figure 6, at time \(t\), only three stations exist; at time \(t+1\), an additional station is added; and at time \(t+2\), the count increases to five stations. Therefore, dynamic multi-graphs are generated for each time interval: \(G_{dis}^{t}(V^{t},\ E^{t},\ A_{dis}^{t})\), \(G_{dis}^{t}(V^{t},\ E^{t},\ A_{dis}^{t})\) and \(G_{poi}^{t}(V^{t},\ E^{t},\ A_{poi}^{t})\).