# A New Approach to Identifying Crash Hotspot Intersections (CHIs) Using Spatial Weights Matrices
## 4 Results and Discussion
### A Performance Comparison of IHA between INDSWMI and IEDSWMI  
As discussed in Section 2.3.1, the inverse Euclidean distance-band spatial weights matrix of intersections (IEDSWMI) can also be used in IHA. Further experimentation of IHA comparing the GIS visualization and Intersection Prediction Accuracy Index (IPAI, as discussed in Section 2.3.3) between the INDSWMI and IEDSWMI was discussed to validate the performance of the proposed approach.  
The crash data of Spencer city for 2008-2014 were used as the training data in the IHA, and the crash data of Spencer city for 2015-2017 were used as the test data in the IPAI calculation. Note that the training and test crash data were both applied in the KDSWMCI generation algorithm to statistically analyze the number of crashes separately. To be more specific, the number of crashes in 2008-2014 at each intersection was used as the training data to identify CHIs. Then, the number of crashes in 2015-2017 at intersections which were within these CHIs was used as the test data to calculate the IPAI. By this approach, the same datasets and the same parameters (as shown in Table 4), except the weights matrix files (INDSWMI and IEDSWMI), were implemented in intersection hotspot analysis at the 95% confidence level, and the IPAI was then measured.  
To contrast them, Figure 12 shows the results of intersection hotspot analysis for the INDSWMI (Figure 12a) and IEDSWMI (Figure 12b). By comparing Figure 12a,b, we can see that the intersection distribution pattern of the CHIs is slightly different. There are fewer CHIs in Figure 11a than in Figure 12b. However, the distribution pattern of roads within the CHIs is notably different. There are much fewer roads within CHIs in Figure 12a than in Figure 12b, which means that the CHIs in Figure 12a have stronger spatial aggregation than those in Figure 12b. These differences are expected since the road network distance of intersections is more appropriate as a distance measurement than the Euclidean distance for IHA.  
Note that the above visual comparison can only qualitatively validate the performance of the proposed approach. In order to quantitatively validate the performance of the proposed approach, the IPAI values of IHA using the INDSWMI and IEDSWMI should be compared. In theory, the higher the IPAI, the better the CHI prediction performance of the approach. The calculated IPAI results, shown in Table 6, indicate that higher prediction accuracy was achieved by IHA with the INDSWMI (IPAI: 4.79) than by IHA with the IEDSWMI (IPAI: 3.45).  
Figure 12: Visual comparison of IHA using the INDSWMI and IEDSWMI.  
Furthermore, an interesting result is indicated: the predicted percentage of crashes in CHIs during 2015-2017 is similar to the identified percentage of crashes in CHIs during 2008-2014 in both IHA with INDSWMI (51.68%-47.90%) and IHA with IEDSWMI (52.42%-48.95%). From this perspective, the results reveal that the CHIs which are identified by this approach have a high probability of being intersections with a high frequency of crashes in the future.