# A New Approach to Identifying Crash Hotspot Intersections (CHIs) Using Spatial Weights Matrices
## 4 Results and Discussion  
### Results  
#### 4.1.1 The INDSWMI of Spencer City  
As described earlier, the SWM is the critical input parameter for hotspot analysis. Therefore, it was necessary to establish the INDSWMI of Spencer city to accurately express the spatial relationships between intersections. The spatial weights (\(W_{ij}\)) of the INDSWMI were calculated based on the network shortest distance along the road segments, as discussed in Section 2.3.1. We take the typical T-intersections and cross-intersections shown in Figure 9 as an example to evaluate the intersection extraction algorithm and demonstrate the INDSWMI of Spencer city. We used the geometric method ST_Intersection, provided by the PostGIS extension, to evaluate the intersection extraction algorithm based on road network topological relationships. When all intersections coincide with the coordinates of the collisions using the geometric method, the accuracy of the intersection extraction algorithm can be verified. We took a typical T-intersection (ID. 921) as an example to demonstrate the evaluation results of the intersection extraction algorithm using the geometric method, as shown in Table 2. The evaluation results successfully demonstrate that the intersection extraction algorithm accurately extracts intersections. Figure 9: Typical T-intersections and cross-intersections. According to a suggestion by [PERSON] and [PERSON] [29], a distance band of 683.64 m was selected to ensure that each intersection had at least one neighbor. Note that the suggestion that each intersection should have at least one neighbor is one of the best-practice guidelines for Getis-Ord Gi* analysis and has been applied to a vast majority of scenarios. However, our distance band of 683.64 m is the result of following the above suggestion for the study area in this research. Therefore, this distance band is not applicable universally and should be adjusted accordingly for different scenarios. Table 3 lists the results under a distance band of 683.64 m, including T-intersections (ID. 584, 921, 1609) and cross-intersections (ID. 113, 1174), created by the INDSWMI generation algorithm (discussed in Section 2.3.2) to save intersections' spatial relationships. Note that Table 3 does not list all the neighbors of intersections (for example, intersection 113 has 97 neighbors under a distance band of 683.64 m) due to space limitations. Generally, the spatial weights (\(W_{\bar{y}}\)) of the INDSWMI were network distance inverted (for example, \(W_{113,\,584}=0.019263\) when the network distance between intersections 113 and 584 is 51.9122 m), so nearer intersections have a larger weight than intersections that are farther away. The columns (objectid, gid, nid, row-standardized weight) in Table 3 can be used to generate the binary swm format file, as discussed in Section 2.2.3. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Intersection id** & **Adjacent Road Segment** & **Collision id** & **Euclidean** & **Coincidence** \\
**and Coordinates** & **id and Coordinates** & **and Coordinates** & **Distance** & **Coincidence** \\ \hline id:921 & id:155 & Collision (155,1238) & & & \\ point (\(-\)95.1464002 & & & Point (\(-\)95.1464002 & 0 & \(\surd\) \\
43.155801) & \(-\)95.146326643.1557037 & & & \\  & id:1238 & Collision (155,1239) & & & \\  & & 43.155801 & & & \\  & & 43.1561124, & & & \\  & & 43.155801) & & & \\  & & 43.155801 & & & \\  & & 43.15611293 & Collision (155,1239) & & \\  & & 43.1561124, & & & \\  & & 43.155801 & & & \\  & & 43.155801 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The evaluation results of the intersection extraction algorithm.