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

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.

Keywords:

• Kernel density estimation
• Network
• Unbiased estimator, Computational complexity
• GIS‐based tool

Acknowledgements

This study was partly supported by the Grant‐in‐Aid for Scientific Research (B), No. 20300098, Japan Society for the Promotion of Science. We thank Mike Batty, Zhixiao Xie and Joni A. Downs for providing us with related papers, and the Chiba Prefecture Police for providing us with traffic accident data. We also thank anonymous referees for their comments on an earlier draft.