Uniform network transformation for points pattern analysis on a non-uniform network

Abstract

In the real world, there are many kinds of phenomena that are represented by points on a network, such as traffic accidents on a street network. To analyse these phenomena, the basic point pattern methods (i.e. the nearest neighbour distance method, the quadrat method, the K-function method and the clumping method) defined on a plane (referred to as the planar basic point pattern methods) are extended to the basic point pattern methods on a network (referred to as the network basic point pattern methods). However, like the planar basic point pattern methods, the network basic point pattern methods assume a uniform network and this assumption is hard to accept when analysing actual phenomena. To overcome this limitation, this paper formulates a transformation, called the uniform network transformation, that transforms a non-uniform network into a uniform network. This transformation provides a simple procedure for analysing point patterns on non-uniform networks: first, a given non-uniform network is transformed into a uniform network; second, the network basic point pattern methods (which assume a uniform network) are applied to this transformed uniform network. No modification to the network basic point pattern methods is necessary. The paper also shows an actual application of this transformation to traffic accidents in Chosei, Japan.