## 4 Local-Global Dynamic Multi-Graph Convolutional Neural Network Model
### Local-Global Dynamic Spatiotemporal Graph Convolution  
The time series of historical bike-sharing demand X = \(\left\{\mathbf{x}_{t_{0}-h+1},\ \mathbf{x}_{t_{0}-h+2},\ \ldots,\ \mathbf{x}_{t_{0}}\right\}\), the station graph network \(G(V,\ E,\ A)\), and spatial semantic feature data (station distances, POI, etc.) are input to the encoder. The dynamic spatiotemporal graph convolution module captures dynamic features in both time and space dimensions. Gated Temporal  
Figure 5: The architecture of LCDMGCN. \(\left\{\mathbf{x}_{t_{0}-h+1},\ \mathbf{x}_{t_{0}-h+2},\ \ldots,\ \mathbf{x}_{t_{0}}\right\}\): the input time series. Records: historical ride records between stations. POI: POIs of stations. Dis: distance between stations. \(\left\{\mathbf{s}_{t_{0}-h+1},\ \mathbf{s}_{t_{0}-h+2},\ \ldots,\ \mathbf{s}_{t_{0}}\right\}\): the feature sequence produced by the encoder. \(Attn\): the output of Temporal Attention. \(\left\{\mathbf{\hat{y}}_{t_{0}-h+1},\ \mathbf{\hat{y}}_{t_{0}-h+2},\ \ldots,\ \mathbf{\hat{y}}_{t_{0}}\right\}\): the predictive sequence.  
Convolution layers are applied in the time dimension, and a Graph Convolutional Neural Network is used in the spatial dimension.  
As shown in Figure 6, the Local-Global Dynamic Spatiotemporal Graph Convolution Module first constructs dynamic multi-graphs with different semantics using the Dynamic Multigraph Generator. These semantics include station distances, historical riding records, station POI information, and information about station dynamic changes. The multiple graphs encompass diverse aspects and varying perspectives of dynamic location semantic information. Merging or concatenating these images into a single model input in a simplistic manner would lead to information loss, thereby failing to capture features on different scales. In the middle section of Figure 6, an example of dynamic multi-graphs can be observed. During time period \(t\), there are three stations (represented by blue solid circles). In time period \(t+1\), the number of stations increases to four (the newly added station on the right changes from a hollow circle to a blue solid circle). In time period \(t+2\), another station is added on the left, making a total of five stations. Secondly, to preserve the diversity and integrity of information to the maximum extent, the dynamic spatiotemporal graph convolution model is divided into two parts: global and local. The Local Spatiotemporal Module focuses on the feature relationships between each station and its adjacent stations, while the Global Spatiotemporal Module focuses on the feature relationships between each station and all other stations. In the upper-middle part of Figure 6, the dynamic distance graph shows connections only between nearby stations (connections between stations are represented by black solid lines, while the connections of absence stations are shown by gray dashed lines). From time period \(t\) to \(t+2\), as the number of stations increases, gray dashed lines become black solid lines, but there will still be no connections between distant stations, such as the leftmost and rightmost stations. Therefore, the dynamic distance graph contains local spatial information, which will be input into the local spatiotemporal module. In contrast, the lower part of Figure 6 shows the dynamic historical connection graph and the dynamic POI similarity graph, which are not limited by distance and thus contain global spatial information. Consequently, these two dynamic multi-graphs are input into the global spatiotemporal module together.  
Here is the overall algorithm flowchart for Local-Global Dynamic Spatiotemporal Graph Convolution Module, as shown in Algorithm 1.  
Figure 6: Local-Global Dynamic Spatiotemporal Graph Convolution Module.