A kernel density estimation method for networks, its computational method and a GIS‐based tool

TLDR

The method can identify hotspots of traffic accidents, street crimes, or pipeline leakages. The study develops a kernel density estimation method for network point density and implements it in a GIS environment. The authors formulate biased and unbiased kernel functions for network density, prove bias properties, and develop computational methods and a GIS plug‑in for efficient implementation. They demonstrate that standard 2D kernels are biased on networks, that their natural extension overestimates node densities, and that the proposed unbiased kernels and computational tools accurately estimate traffic‑accident densities, offering practical guidance.

Abstract

We develop a kernel density estimation method for estimating the density of points on a network and implement the method in the GIS environment. This method could be applied to, for instance, finding ‘hot spots’ of traffic accidents, street crimes or leakages in gas and oil pipe lines. We first show that the application of the ordinary two‐dimensional kernel method to density estimation on a network produces biased estimates. Second, we formulate a ‘natural’ extension of the univariate kernel method to density estimation on a network, and prove that its estimator is biased; in particular, it overestimates the densities around nodes. Third, we formulate an unbiased discontinuous kernel function on a network. Fourth, we formulate an unbiased continuous kernel function on a network. Fifth, we develop computational methods for these kernels and derive their computational complexity; and we also develop a plug‐in tool for operating these methods in the GIS environment. Sixth, an application of the proposed methods to the density estimation of traffic accidents on streets is illustrated. Lastly, we summarize the major results and describe some suggestions for the practical use of the proposed methods.