# A New Approach to Identifying Crash Hotspot Intersections (CHIs) Using Spatial Weights Matrices
## 1 Introduction  
The nation's transportation infrastructural systems are deteriorating [1] under adverse influences from multiple factors, such as corrosion [2; 3], aging [4], impact [5; 6], and vibration [7], and even with the recent advances in structural health monitoring [8; 9; 10] and intelligent transportation systems [11; 12], traffic crashes still happen. The latest quick facts report from the National Highway Traffic Safety Administration indicates that there were 2,746,000 people injured in 6,452,000 police-reported crashes in 2017 in the USA [13]. As junctions of traffic flow and pedestrian flow, intersections with ancillary facilities have an important impact on the frequency of crashes. Intersection-related crashes, which account for a large portion of all crashes, need more research attention. For example, Iowa, USA, saw about 225,185 intersection-related crashes, about 40.41% of all crashes, from 2008 to 2018 [14]. Given the fact of the massive number of intersections, identifying crash hotspot intersections (CHIs) is an important but challenging task. A review of previous studies shows that the Getis-Ord Gi*, well known in hotspot analysis, has been commonly used to detect crash hotspots [15]. Hotspot analysis examines the Getis-Ord Gi* statistic [16; 17], a local indicator of spatial autocorrelation developed by Professor [PERSON] and [PERSON], for individual crashes based on a comparison with neighboring crashes to quantitativelydescribe crashes and hotspot areas where crashes are mainly concentrated. [PERSON] et al. [18] discussed the identification of hot zones and enhanced the capability to examine a given highway by determining dangerous segments. [PERSON] et al. [19] used the Getis-Ord Gi* statistic to analyze weather-related crashes which occurred in adverse weather conditions. [PERSON] et al. [20] assessed the spatial clustering of accidents and hotspots' spatial densities using the Getis-Ord Gi* statistic. [PERSON] et al. [21] compared traditional hotspot detection methods with spatial statistical methods, including the Getis-Ord Gi* statistic, in terms of their sensitivity to spatial characteristics of crash clusters. [PERSON] et al. [22] combined kernel density estimation and Getis-Ord Gi* maps to identify high-risk areas for traffic crash hotspots and crime events. [PERSON] et al. [23] presented a new method to evaluate the application of four different hotspot analysis methods, such as Getis-Ord Gi*, in ArcGIS 10.2 to identify and rank hotspots using historical data on a section of a road in Brunei Darussalam. [PERSON] [24] et al. used hotspot analysis (Getis-Ord Gi*) and the kernel density method to identify traffic accident hotspots for traffic safety. The above studies focused on using the Getis-Ord Gi* statistic to identify crash hotspots. Unlike crash hotspot analysis, only a limited number of studies have been dedicated to analyzing the spatial relationships between intersections and traffic crashes. [PERSON] [25] indicated that unstructured effects were somewhat significant at the intersection level for cases of severe-injury crashes. [PERSON] et al. [26] presented a crash evolution characteristic analysis for identifying hotspots among Wujiang's road intersections. [PERSON] et al. [27] examined the potential associations between violations made by pedestrians and motorists at intersections. Furthermore, the results of hotspot analysis using the Getis-Ord Gi* statistic in the above research were determined using critical input spatial weights matrices (SWMs) [28; 29]. The related theories of general SWMs, such as contiguity-based SWMs [30; 31], distance-band SWMs [32; 33], and k-nearest neighbor SWMs [34], have been widely discussed. However, the general SWMs, which are designed for plane space, cannot provide good support for hotspot analysis in road network space. Therefore, we should improve the construction algorithms and build customized SWMs based on the above general SWM to adapt the identification approach of CHIs. The above studies provide a foundation for this research.