# Short-Term Passenger Flow Prediction of Urban Rail Transit Based on a Combined Deep Learning Model
## 4 Analysis of Passenger Flow Characteristics and Influencing Factors of URT
### Analysis of Factors Affecting Passenger Flow  
The change of URT short-term passenger flow is affected by many factors. It presents an overall law that is based on its own long-term evolution and has certain periodic and random fluctuations. Actually, not all factors have a large impact on passenger flow. Some factors such as whether it rains have a great impact on residents' travel, which even determines the peak of the passenger flow. Some factors have little impact on passenger flow, and whether to consider them or not has no effect on the accuracy of passenger flow prediction. To achieve an accurate prediction of the short-term passenger flow of URT, it is necessary to select appropriate relevant influencing factors. The following uses the Pearson correlation coefficient analysis to determine the factors that have an impact on the passenger flow. The Pearson coefficient can measure the degree of linear correlation between two variables, so as to filter out irrelevant factors with less influence [39]. Its calculation formula is as formula (9):  
\[\rho_{x,y}=\frac{Cov(X,Y)}{\sigma_{x}\sigma_{y}}=\frac{E(XY)-E(X)E(Y)}{\sqrt{E( X^{2})-E^{2}(X)}\sqrt{E(Y^{2})-E^{2}(Y)}} \tag{9}\]  
where \(\rho_{x,y}\) is the Pearson correlation coefficient; \(X\) is the passenger flow; \(Y\) is the corresponding influencing factors; \(Cov(X,Y)\) is the covariance of \(X\) and \(Y\); \(\sigma_{x}\) and \(\sigma_{y}\) are the standard deviation of \(X\) and \(Y\), respectively; \(E(X)\) and \(E(Y)\) are the mathematical expectations of \(X\) and \(Y\), respectively; \(E(XY)\) is the mathematical expected value after multiplying the corresponding variables of \(X\) and \(Y\). The Pearson correlation coefficient \(\rho_{x,y}\) has a value between \(-1\) and \(1\). The larger the absolute value, the stronger the correlation between the influencing factor and the passenger flow, and vice versa. The positive and negative values of \(\rho_{x,y}\) represent different correlations, with greater than \(0\) representing positive correlation and less than \(0\) representing negative correlation. The Pearson correlation coefficients calculated from the data are shown in Table 2.  
Given the influence of date attributes on passenger flow, it can be seen that the passenger flow of rail transit fluctuates depending on whether it is a working day and the passenger flow of the previous day. Daily passenger flow data and daily average passenger flow data within a week were selected for analysis, and the results are shown in Figure 9. It can be seen from Figure 9 that the peak passenger flow at weekends is significantly lower than that on working days. There is also a certain fluctuation in the peak passenger flow between two adjacent days during the week, which indicates that the date attribute has a great influence on the passenger flow. The Pearson correlation coefficient calculated according to the specific data is shown in Table 2. It can be seen that the two influencing factors of daily average passenger flow on working days and weekend holiday attributes are at a level of \(p<0.01\) (within the 99% confidence interval). The correlation is significant, and the correlation of the weekend holiday attribute is stronger than that of average daily passenger flow on working days. \begin{table}
\begin{tabular}{l c c} \hline \hline \multirow{2}{*}{**Relevant Influencing Factors**} & **Pearson Correlation** & \multirow{2}{*}{**Significance (Two-Tailed)**} \\  & **Coefficient** & \\ \hline Average daily passenger flow & \(0.710\) & \(0.000\) \\ on weekdays & \(-0.915\) & \(0.000\) \\ Weekend holiday properties & \(-0.213\) & \(0.008\) \\ Passenger flow per hour & \(-0.747\) & \(0.000\) \\ Weather conditions & \(-0.354\) & \(0.003\) \\ Wind power & \(-0.023\) & \(0.290\) \\ Air quality index & \(-0.235\) & \(0.005\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Pearson correlation coefficient of factors affecting passenger flow. The passenger flow of URT is time series data.