# A Two-Phase Approach for Predicting Highway Passenger Volume
## 5 Phase I: Extraction of Significant Factors  
In Phase I, the RF algorithm was used for removing the highly correlated impact factors and extracting the significant impact factors. Specifically, impact factors with a high importance degree were retained and those with a low importance degree were removed. The RF algorithm has the advantage of showing the extraction of significant factors step by step and the extracted significant impact factors are interpretable, compared with some auto-encoder methods like neural networks. Finally, a dataset of significant impact factors was built for predicting highway passenger volume.  
Firstly, the correlation coefficients between impact factors were calculated by correlation analysis, and fifteen groups of highly correlated impact factors were found based on the calculated correlation coefficients, which are shown in Table 1.  
Then, the importance degree of highly correlated impact factors in each group was calculated with the RF algorithm, as shown in Figure 3. The horizontal axis represents impact factors in each group, and the vertical axis represents the corresponding importance degree. Only the impact factor with the largest importance degree in each group was retained, and other impact factors were removed. Consequently, 28 impact factors, including NSS, NSSP, NSP, SC, DRSC, TSP, DCAB, DPFI, DPFE, PFI, FC, DDB, DHD, DLB, LB, DGIO, IFA, DIFA, DIFA, DIBE, WS, ECI, AEC, PB, NT, GCA, AGL, DNBH, and NH, were removed and the other 41 impact factors were retained. Then, the importance degree of the remaining impact factors was calculated again and sorted in order, as shown in Figure 4.  
In this study, the removed proportion was set at 10%. Therefore, impact factors with importance degree rankings in the bottom 10% were removed. According to Figure 4a, the removed impact factors included RP, CPR, VISR, and DNH, and the remaining 37 impact factors were retained for the subsequent data processing.  
Similarly, the importance degree of impact factors was calculated repeatedly and sorted in order, and impact factors whose importance degree ranked in the bottom 10% were removed until the importance degree of the remaining impact factors reached 0.01. The above process was repeated twice. PCGRP, IRE, LA, and PFE, and DPD, PTPT, and CLPGR were removed during these two processes, respectively, as seen in Figure 4b,c. Finally, a total of 30 impact factors were retained, and are shown in Table 2. The category of resource and environment had more retained factors than any other, indicating that this category has a significant impact on highway passenger volume. Moreover, the importance degrees of HD, GDP, WCS, NOB, RT, HEC, TP, and TI rank in the top 25%, meaning that these eight factors significantly impact highway passenger volume.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Group** & **Highly Correlated Impact Factors** & **Group** & **Highly Correlated Impact Factors** \\ \hline
1 & NSS, NSP, NSSP, TP & 8 & DLB, HD \\
2 & RT, SC, DRSC, TSP & 9 & GIO, DGIO \\  & & 10 & IFA, DIFA, IRE, DIRE \\
3 & DLA, DCAB & 11 & WS, WCS \\
4 & FC, PFI, PFE, DPFI, DPFE & 12 & AEC, ECI, HEC \\
5 & DB, DDB & 13 & NOB, PB, NT \\
6 & HD, DHD & 14 & AGL, APGL, GCA \\
7 & LB, DLB & 15 & NH, NBH, DNBH \\ \hline \hline \end{tabular}
\end{table}
Table 1: Groups of highly correlated impact factors.  
Figure 3: The importance degrees of significantly correlated variables in each group.  
Figure 4: Importance degrees of impact factors. (**a**) The first iteration. (**b**) The second iteration. (**c**) The third iteration.