Outline

This method is preformed on crashes that occur on a single roadway and uses the mile post to preform kernel density estimation (KDE) of crashes along that road way. The KDE curve provides a smoothed curve indicating mile posts with high crash frequency, finding the local maxima of this curve provides specific mile posts where clusters are likely. Crashes are then assigned to the closest maxima.

With crashes assigned to a maxima clusters are identified by using a search distance. A crash can only be part of a cluster if it is within the search distance of a maxima or within the search distance of a crash that is within the cluster. For example, if we have crashes at mile posts 1.1, 1.5, 3.2, 3.3, 3.5, 3.7, and 4.5 producing maxima of 1.2, 3.35, and 4.5 the crashes would be assigned as follows using a search distance of 0.25 miles:

Crash MP Maxima Cluster
1.1 1.2 True
1.5 1.2 False
3.2 3.35 True
3.3 3.35 True
3.5 3.35 True
3.7 3.35 True
4.5 4.5 True

The crash at 1.5 is not a part of a cluster as it is 0.3 miles from the maxima, the crash at 3.7 is a part of a cluster however as it is within the search distance of the crash at 3.5 which is only 0.15 miles from the maxima.

Finally a cluster must consist of a minimum number of crashes. With the clusters identified the maximum and minimum crash mile posts are reported and can be used to map the cluster on a linear reference system.The search distance and minimum number of crashes can be adjusted.

Example

Crash Density

These plots are for pedestrian crashes on route R-VA US00250EBBUS001, which consists of 17 crashes along 3.5 miles. The density curve is below.

With the densities plotted a spline can be fitted to the density curve which allows local maxima to be calculated using the second derivative of the curve, providing the following maxima: 0.90, 2.54, 3.3. Which can be seen on the curve below.

The following shows the results of the clustering analysis:

Crash MP Maxima Distance to Maxima Distance to Neighbor In Distance Cluster Count Cluster
0.86 0.90 0.04 0.68 True 1 False
1.54 0.90 0.64 0.68 False NA False
1.87 2.54 0.67 0.19 True 11 True
1.87 2.54 0.67 0.19 True 11 True
2.06 2.54 0.48 0.15 True 11 True
2.21 2.54 0.33 0.07 True 11 True
2.28 2.54 0.26 0.21 True 11 True
2.49 2.54 0.05 0.01 True 11 True
2.5 2.54 0.04 0.17 True 11 True
2.67 2.54 0.13 0.01 True 11 True
2.68 2.54 0.14 0.07 True 11 True
2.68 2.54 0.14 0.07 True 11 True
2.75 2.54 0.21 0.07 True 11 True
3.24 3.3 0.06 0.17 True 4 False
3.41 3.3 0.11 0.09 True 4 False
3.5 3.3 0.2 0.0 True 4 False
3.5 3.3 0.2 0.0 True 4 False

There is one cluster of 11 crashes between mile post 1.87 and 2.75, if the minimum number was lowered to 4 there would be a second cluster between 3.24 and 3.5.