Optimizing Kernel Density Estimation Bandwidth for Road Traffic Accident Hazard Identification: A Case Study of the City of London
Abstract
:1. Introduction
2. Materials and Methods
2.1. Study Area and Data
2.2. Methodology
2.2.1. Overview of the Method
- (1)
- Collection of traffic accident data, including crash coordinates, road network data, and casualty information, followed by data screening and preliminary processing;
- (2)
- Determination of crash hazard level, which serves as the analytical indicator for the identification of crash hazard hotspots. Crash hotspots identified based on this indicator are defined as crash hazard hotspots;
- (3)
- Verification of the spatial point distribution pattern using the nearest neighbor index (NNI) to test the clustering characteristics of crash points within the study area and providing a prerequisite for planar KDE analysis;
- (4)
- Determination of the optimal bandwidth using ArcGIS’s automatic extraction method, multi-distance spatial cluster analysis (Ripley’s K-function), and ISA analysis to calculate the bandwidth, obtaining planar KDE results under different bandwidths and further introducing the PAI to determine the optimal bandwidth for planar KDE;
- (5)
- Model validation and extension: identifying crash hazard hotspots using the optimized bandwidth of planar KDE and drawing their distribution maps and analyzing the accuracy of the results.
2.2.2. Crash Hazard Level
2.2.3. Average Nearest Neighbor (ANN) Analysis
2.2.4. Kernel Density Estimation (KDE)
2.2.5. Multi-Distance Spatial Cluster Analysis (Ripley’s K-Function)
2.2.6. Incremental Spatial Autocorrelation (ISA) Analysis
2.2.7. Predictive Accuracy Index (PAI)
3. Results
3.1. ANN Analysis Results
3.2. Multi-Distance Spatial Cluster Analysis (Ripley’s K-Function)
3.3. Incremental Spatial Autocorrelation Analysis
3.4. ArcGIS Automated Extraction
3.5. Bandwidth Optimization
- (a)
- With the default bandwidth, the hotspots are small and dispersed, potentially underestimating the spatial overflow effect of crash risks.
- (b)
- The optimal bandwidth obtained from multi-distance spatial cluster analysis results in larger and overly smooth hotspots, masking local high-risk areas.
- (c)
- The hotspot distribution under the optimal bandwidth obtained from ISA analysis is relatively balanced, striking a better balance between local concentration and overall continuity of hotspots.
3.6. Crash Hazard Hotspot Identification and Analysis (Test Data)
3.7. Crash Hazard Hotspot Identification (Validation Data)
4. Discussion
4.1. Traffic Crash Data
4.2. Crash Hazard Level
4.3. Kernel Density Bandwidth
4.4. Hotspot Identification
5. Conclusions
- (1)
- The NNI of the test data within the study area was 0.448, which was less than 1. The corresponding Z-score was −27.007, and the p-value was far less than 0.01. This indicated that the spatial distribution pattern of crash points exhibited a significant clustering characteristic rather than a dispersion characteristic.
- (2)
- The bandwidth values obtained from the test data using ArcGIS automatic extraction, multi-distance spatial cluster analysis (Ripley’s K-function), and ISA analysis were 52.8 m, 189.428 m, and 134 m, respectively. The corresponding PAI values were 3.459, 4.082, and 4.381, respectively. Among these, the ISA analysis yielded the highest PAI value, indicating that the determined bandwidth of 134 m was the optimal value. With this bandwidth, the planar KDE method accurately predicted and identified the traffic crash hazard hotspots in the City of London. The predicted hotspots exhibited a balanced distribution and reflected both the local concentration and overall continuity of hotspots. This suggested that the chosen bandwidth effectively captured the spatial patterns of crash risks, providing a reliable measure for sustainable road safety assessment and management in the study area.
- (3)
- To quantitatively rank the identified crash hazard hotspots, several factors can be considered, including the number of crashes within each hotspot, the hazard level of the hotspots, and the kernel density estimates. These quantitative measures allow for a comparison of the crash risk levels among different hotspots, enabling the identification of areas requiring prioritization and providing targeted evidence for developing sustainable traffic safety improvement measures within them.
- (4)
- The utilization of the optimal bandwidth value of 134 m on the validation data demonstrated the ability to identify most high-risk areas. The distribution of crash hazard hotspots was largely consistent with the results obtained from the test data. Moreover, the method can identify potential crash hazard hotspots caused by environmental traffic factors. These findings indicated that the proposed method exhibits good reliability, accuracy, and robustness at a medium-term to long-term scale.
- (5)
- The identification of crash hazard hotspots can be integrated into intelligent transportation management to establish a comprehensive traffic safety management model that achieves the sustainability of transportation systems across the “prevention, control, and evaluation” stages, aimed at continuously enhancing the safety and environmental adaptability of urban road traffic systems.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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OBJECTID | ExpectedK | ObservedK | DiffK | LwConfEnv | HiConfEnv |
---|---|---|---|---|---|
1 | 127 | 183.105733 | 56.105733 | 120.158208 | 126.275048 |
2 | 130 | 186.040716 | 56.040716 | 123.182899 | 129.179362 |
3 | 133 | 189.428114 | 56.428114 | 125.971586 | 131.997496 |
4 | 136 | 192.32785 | 56.327850 | 128.447979 | 134.406691 |
5 | 139 | 195.395571 | 56.395571 | 131.371488 | 137.289097 |
6 | 142 | 197.910726 | 55.910726 | 134.187466 | 140.385117 |
7 | 145 | 200.409007 | 55.409007 | 136.924051 | 143.414315 |
8 | 148 | 202.949072 | 54.949072 | 139.733479 | 146.058682 |
9 | 151 | 205.701196 | 54.701196 | 142.755882 | 149.15032 |
10 | 154 | 208.275673 | 54.275673 | 145.331213 | 152.159813 |
OID | Distance | Moran’s I | Expected I | Variance | Z-Score | p Value |
---|---|---|---|---|---|---|
0 | 110 | 0.031638 | −0.001560 | 0.000492 | 1.497267 | 0.134324 |
1 | 116 | 0.030261 | −0.001553 | 0.000462 | 1.480205 | 0.138818 |
2 | 122 | 0.033616 | −0.001550 | 0.000431 | 1.693919 | 0.090281 |
3 | 128 | 0.035998 | −0.001548 | 0.000402 | 1.872998 | 0.061069 |
4 | 134 | 0.040079 | −0.001546 | 0.000378 | 2.140632 | 0.032304 |
5 | 140 | 0.032162 | −0.001541 | 0.000355 | 1.789074 | 0.073603 |
6 | 146 | 0.031515 | −0.001538 | 0.000318 | 1.852972 | 0.063886 |
7 | 152 | 0.028327 | −0.001536 | 0.000297 | 1.732003 | 0.083273 |
Method (Bandwidths) | Total Crashes | Crashes | Percentage of Crashes (%) | Total Area (km2) | Area (km2) | Percentage of Area (%) | PAI |
---|---|---|---|---|---|---|---|
ArcGIS automatic Extraction-52.8 m | 655 | 76 | 11.603 | 2.892 | 0.097 | 3.354 | 3.459 |
Ripley’s K-function-189.428 m | 655 | 294 | 44.885 | 2.892 | 0.318 | 10.996 | 4.082 |
ISA-134 m | 655 | 229 | 34.962 | 2.892 | 0.231 | 7.981 | 4.381 |
No. | Crash Hazard Hotspot ID | Area m2 | Number of Crashes in Hotspots | Hotspot Hazard Levels | Unit Kernel Density Estimates |
---|---|---|---|---|---|
1 | 1 | 59,964 | 65 | 115 | 0.046838 |
2 | 3 | 47,665 | 51 | 103 | 0.038729 |
3 | 8 | 53,764 | 51 | 98 | 0.037935 |
4 | 5 | 18,730 | 16 | 26 | 0.030833 |
5 | 6 | 12,182 | 14 | 23 | 0.030304 |
6 | 7 | 16,167 | 13 | 36 | 0.031051 |
7 | 2 | 8433 | 12 | 17 | 0.028719 |
8 | 9 | 8047 | 5 | 22 | 0.030276 |
9 | 4 | 5579 | 2 | 2 | 0.027396 |
No. | Crash Hazard Hotspot ID | Area m2 | Number of Crashes in Hotspots | Hotspot Hazard Levels | Unit Kernel Density Estimates |
---|---|---|---|---|---|
1 | 1 | 39,466 | 48 | 90 | 0.024252 |
2 | 3 | 66,756 | 31 | 78 | 0.023539 |
3 | 8 | 53,029 | 31 | 78 | 0.023464 |
4 | 5 | 23,479 | 14 | 19 | 0.015603 |
5 | 7 | 27,996 | 10 | 21 | 0.015993 |
6 | 2 | 39,300 | 9 | 20 | 0.015723 |
7 | 4 * | 28,397 | 8 | 23 | 0.018698 |
8 | 9 | 11,802 | 7 | 15 | 0.015225 |
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Zheng, M.; Xie, X.; Jiang, Y.; Shen, Q.; Geng, X.; Zhao, L.; Jia, F. Optimizing Kernel Density Estimation Bandwidth for Road Traffic Accident Hazard Identification: A Case Study of the City of London. Sustainability 2024, 16, 6969. https://doi.org/10.3390/su16166969
Zheng M, Xie X, Jiang Y, Shen Q, Geng X, Zhao L, Jia F. Optimizing Kernel Density Estimation Bandwidth for Road Traffic Accident Hazard Identification: A Case Study of the City of London. Sustainability. 2024; 16(16):6969. https://doi.org/10.3390/su16166969
Chicago/Turabian StyleZheng, Minxue, Xintong Xie, Yutao Jiang, Qiu Shen, Xiaolei Geng, Luyao Zhao, and Feng Jia. 2024. "Optimizing Kernel Density Estimation Bandwidth for Road Traffic Accident Hazard Identification: A Case Study of the City of London" Sustainability 16, no. 16: 6969. https://doi.org/10.3390/su16166969