# A Multiview Representation Learning Framework for Large-Scale Urban Road Networks
## 5 Analysis and Discussions  
### Information Evaluation of the Representations  
The information evaluation comprises two parts. One part aims to verify that the walk process on the partitioned subgraphs is information lossless, and the other part strives to verify that the representations produced by our framework can contain more information than that contained in the representation produced by baseline methods.  
Figure 7 shows two frequency distributions of nodes in three subgraphs via two colors. The two frequency distributions are calculated from random walk sequences based on the original and partitioned subgraphs. It is evident that the two frequency distributions in the different subgraphs are almost the same, which suggests that the proposed road network organization does not affect the information that is expressed by each node in the multiview random walk process.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**ETA Methods**} & \multirow{2}{*}{**Dataset**} & \multirow{2}{*}{**DeepWalk**} & \multirow{2}{*}{**Node2 Vec**} & \multirow{2}{*}{**Road2 Vec**} & \multirow{2}{*}{**Our Framework**} \\ \cline{3-4} \cline{6-7}  & & **MAPE/RMSE/MAE** & & & & \\ \hline \multirow{2}{*}{GRU} & Shenzhen & 15.26/168.74/112.31 & 15.58/172.03/**106.45** & 14.70/162.88/115.85 & **14.59**/**158.97**/113.785 \\  & Xi’an & 3.53/119.48/102.50 & 5.36/104.47/90.05 & 3.20/72.11/68.95 & **2.76**/**54.31**/**43.76** \\ \hline \multirow{2}{*}{GRU + DNN} & Shenzhen & 13.93/151.95/106.78 & 13.89/**151.80**/110.84 & 13.71/154.30/108.06 & **13.66**/154.13/**106.51** \\  & Xi’an & 2.69/48.88/44.26 & 2.05/31.39/27.71 & 2.39/28.62/22.04 & **1.87**/**23.96**/**19.42** \\ \hline \multirow{2}{*}{DeepTTE} & Shenzhen & 13.92/159.96/112.31 & 13.84/152.24/106.45 & 13.82/155.28/108.0 & **13.54**/**152.20**/**106.34** \\  & Xi’an & 14.22/154.02/133.50 & 12.52/88.35/71.43 & 13.39/91.25/70.96 & **12.13**/**86.54**/**68.03** \\ \hline \multirow{2}{*}{WDR} & Shenzhen & 13.53/148.29/104.07 & 13.49/151.53/105.71 & 13.50/149.52/104.53 & **13.46**/**147.84**/**103.92** \\  & Xi’an & 3.67/**35.80**/**26.65** & 4.16/55.31/46.14 & 5.10/50.48/37.86 & **3.51**/49.93/38.07 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Results of the baseline methods and our framework in the ETA determination task on the two datasets.  
Figure 7: Frequency distribution of each node in three subgraphs: (**a–c**) via the sequences generated based on the original multigraph (blue line) and partitioned subgraphs (orange line).  
Furthermore, for each representation vector, there are three distances. One distance is the cosine distance in latent space, the second distance is the topological distance, and the third distance is the transition probability in human mobility. If the representation is topology aware, the smaller the topological distance between road segments, the smaller the cosine distance is between their corresponding vectors. As illustrated in Figure 8a, although all the methods can preserve topological information, our framework can preserve a larger amount. In our framework, the rate of change of the cosine distance with respect to the topological distance of the road segment is the most obvious and the most uniform. Additionally, if the representation is mobility aware, the lower the transition probability between road segments, the larger the cosine distance is between their corresponding vectors. As shown in Figure 8b, DeepWalk and Node2 Vec lack the ability to preserve human mobility information, while our framework and Road2 Vec can distinguish different transition probabilities in human mobility based on the cosine distance. However, when the transition probability is high (>0.8), the performance of Road2 vec is low, and the trend of the curve abruptly changes within this interval. Based on the above analysis, compared to the baseline methods, our framework can preserve both topological and human mobility information.