# Multi-Scale Residual Depthwise Separable Convolution for Metro Passenger Flow Prediction
## 2 Methodology  
### Overall Framework  
This study aims to predict the inflow and outflow of passengers based on historical metro passenger flow data and predefined graph structure data. Assuming there are \(N\) metro stations in the network, the passenger flow at time interval \(t\) is denoted as \(X_{t}\in R^{N\times 1}\). The previous \(\tau\) time step historical passenger flow data across the entire metro system are represented as a signal \(X_{T}\in R^{N\times\tau}=(X_{t-\tau},X_{t-\tau+1},X_{t-\tau+2},\cdots,X_{t})\), \(T=\{t-\tau,t-\tau+1,t-\tau+2,\cdots,t\}\), a series of time intervals, whereby \(\tau\), \(\tau+1\), and \(\tau+2\) represent different time offset values from the current time interval \(t\) to the past. Aiming to efficiently capture the trends of passenger flow across various time periods (real-time, daily, and weekly), our model contains three different types of temporal patterns \(X_{T}^{p}(p=r,d,w)\). The passenger flow data of \(N\) metro stations in \(T\) time intervals can be defined as \(X=\left(X_{T}^{r},X_{T}^{d},X_{T}^{w}\right)\), whereby \(X_{T}^{r}\), \(X_{T}^{d}\), and \(X_{T}^{w}\) represent the passenger inflow or outflow in the three temporal patterns mentioned above, respectively.  
The inter-station correlation not only represents the connection between adjacent stations but also represents the correlation between station passenger flow trends in the metro network. Station interaction graphs are constructed to capture inter-station correlations based on network structure correlation graph \(G_{c}=(V,E_{c},A_{c})\) and passenger flow similarity graph \(G_{s}=(V,E_{s},A_{s})\), where \(V=(v_{1},v_{2},\cdots,v_{n})\) is the set of stations, and \(E_{c}\) and \(E_{s}\) are the set of edges that depict connections between stations in different graphs. \(A=\{(i,j,a(i,j))|i,j\in V,i\
eq j\}\) is denoted as adjacency matrix, indicating the weights of the edge from station \(v_{i}\) to station \(v_{j}\). \(A_{c}\) is the adjacency matrix of \(G_{c}\), and the adjacency matrix of \(G_{s}\) is represented by \(A_{s}\in R^{N\times N}\), which is the normalized result of the passenger flow similarity matrix. The main purpose of this study is to perform network-level prediction for passenger inflow and outflow by the data matrices \(X\) and the station interaction graphs \(G_{c}\) and \(G_{s}\).  
The framework of the MRDSCNN model is depicted in Figure 1, encompassing RDSC module, MDSC module, and AttBiGRU module. The RDSC module cleverly utilizes the residual structure of hopping connections and integrates stacked residual blocks in three different temporal modes. The residual block incorporates a channel mechanism, which focuses on the important temporal dynamics features of metro passenger flow. Meanwhile, the MDSC module utilizes multi-scale convolution to extract complex inter-station correlations from network structure correlation graph and passenger flow similarity graph. This strategy empowers the model to capture features at different scales and enhances fine-grained feature modeling. Then, the outputs of the above modules are integrated through the fusion layer and fed into AttBiGRU to learn the global evolutionary features of all stations. Notably, the adoption of depthwise separable convolution (DSC) effectively reduces parameter overhead and maintains predictive performance.