# An Arch-Bridge Topology-Based Expressway Network Structure and Automatic Generation
## 4 Experiment and Results Analysis
### Evaluation of Road Network Topology Reconstruction  
To evaluate the effectiveness of the proposed method, we compared the automatically generated road network topology with the actual topology of the expressway network and used precision and recall to quantify the evaluation. Specifically, the precision of the method is determined by the excess topology generated in the reconstructed topology, with fewer excess unmatched topologies indicating higher precision, as shown in the following formula:  
\[precision=1-\frac{\#FP}{\#TP+\#FP} \tag{16}\]  
where \(\#TP\) and \(\#FP\) indicate the number of correct topologies identified as correct topologies and the number of incorrect topologies identified as correct topologies in the generated topology set, respectively.  
Likewise, the recall is determined by the number of unmatched topologies in the actual topology of the expressway network, with fewer unmatched topologies indicating higher recall, as shown in the following formula:  
\[recall=1-\frac{\#FN}{\#TP+\#FN} \tag{17}\]  
where \(\#FN\) indicates the number of unmatched topologies in the actual topology of the expressway network.  
Figure 6: The relationship between data size and topology coverage.  
Precision and recall are conflicting measures. \(F1\) is a comprehensive indicator calculated from precision and recall:  
\[F1=2\cdot\frac{recall\cdot precision}{recall+precision} \tag{18}\]  
The \(F1\) value ranges from 0 to 1, with a higher value indicating better performance in generating gantry topologies. When \(F1\) is equal to 1, that is, when both recall and precision are equal to 1, this indicates that the topology of the expressway network has been fully reconstructed.  
In this section, we generated a candidate topology set using a dataset of 1 million records and evaluated the optimization results using quantitative metrics and visualization techniques. As shown in Figure 6(a), although the recall rate was 0.981 before optimization, the precision and \(F1\) scores were only 0.683 and 0.805, respectively. When projected onto a map, the resulting road network displayed disorderly and irregular patterns, with numerous anomalous topologies. However, after optimization, Figure 6(b) shows that the anomalous topologies were effectively removed and all evaluation indicators were superior to those before optimization. Specifically, the precision reached 0.966 and the \(F1\) value reached 0.974.  
We further delved into the evaluation of topological coverage and recall rates. Figure 8 illustrates that under various levels of topological coverage, the topological recall rate is always greater than or equal to the topological coverage rate. Specifically, the corresponding recall rates were 0.34, 0.57, 0.74, 0.89, and 0.98 when the topological coverage was 0.2, 0.4, 0.6, 0.8, and 0.98, respectively. In other words, the recall was improved by 0.14, 0.17, 0.14, 0.08, and 0 for a topological coverage of 0.2, 0.4, 0.6, 0.8, and 0.98, respectively. This demonstrates that the proposed method not only identifies topologies that appear in the trajectory but also generates topologies that do not appear. Notably, when the topological coverage is low, the proposed method's recall rate is more significant.  
Figure 7: Visualization of road network topology.