# A New Approach to Identifying Crash Hotspot Intersections (CHIs) Using Spatial Weights Matrices
## 5 Conclusions  
Intersections have an important impact on the frequency of crashes. In this paper we successfully demonstrated an approach to directly identify crash hotspot intersections (CHIs) using spatial weights matrices (SWMs). The application of this methodology was illustrated by using a spatial data set, including roads and traffic crashes, of Spencer city, Iowa, USA. The proposed inverse network distance-band spatial weights matrix of intersections (INDSWMI) generation algorithm uses the network distance matrix of intersections (NDMI) and a distance band to conceptualize the spatial relationships between intersections with respect to road network restraints. The developed k-nearest distance-band spatial weights matrix between crash and intersection (KDSWMCI, k = 1) generation algorithm has the ability to aggregate the crashes with intersections by considering GPS location accuracy. The INDSWMI generation algorithm can also be applied to building the SWM of road network crashes with the added value that it can be used to support further spatial analysis (e.g., high-low clustering and Local Moran's I analysis). As a major contribution, we developed the Intersection Prediction Accuracy Index (IPAI) to test the prediction performance of intersection hotspot analysis (IHA). According to the findings of a performance comparison between IHA with the INDSWMI and IHA with the inverse Euclidean distance-band spatial weights matrix of intersections (IEDSWMI), the proposed approach has higher accuracy in identifying CHIs.  
The potential of this study can be further realized if we address the following two issues in our future work. First, in this study, the crashes were applied in the proposed approach without consideration of the different crash types. Crashes can be divided into different types--vehicle rollover, single-car accident, rear-end collision, side-impact collision, and head-on collision--and each type may have a different spatial pattern. It is necessary to differentiate the treatment of crashes according to different types. As such, we will develop a spatial data mining approach considering different types of crashes to discover the different spatial patterns of crashes. Second, in the current approach, the IPAI was tested with one distance band chosen to ensure that each intersection had at least one neighbor. However, the selection of a different distance band according to a different minimum neighbor count may have some influence on the prediction accuracy of the proposed approach. As such, in future work we will analyze the prediction accuracy of the IHA with different distance bands and suggest a distance band selection to maximize the prediction performance of the proposed approach.  
[PERSON] and [PERSON] developed the original idea. [PERSON] and [PERSON] proposed the method. [PERSON] and [PERSON] analyzed the data. [PERSON] and [PERSON] wrote the paper. [PERSON] proofread and revised the paper. All authors have read and agreed to the published version of the manuscript. This work was supported by the Construction Science and Technology Program of Hubei Province in 2016 (Transportation, municipal No. 02) and the Research Start-Up Funding of Hubei University of Education Grant NO. 18 RC09.  
\begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline  & **Number of Crashes** & **Percentage** & **Number of Crashes** & **Percentage** & **Total Length of Roads** & **Percentage of Total Length** & **IPAI** \\  & **in CHIs** & **in CHIs** & **in CHIs** & **in CHIs** & **within** & **of Roads** & **within CHIs** & \\ \hline IHA with & & & & & & & \\ INDSWMI & 29 & 51.68\% & 137 & 47.90\% & 24,115.51 & 10.01\% & 4.79 \\ \hline IHA with & & & & & & & \\ IEDSWMI & 30 & 52.42\% & 140 & 48.95\% & 34,198.16 & 14.19\% & 3.45 \\ \hline \hline \end{tabular}
\end{table}
Table 6: The IPAI and the percentage of CHIs predicted.