A Point Pattern Network Density Algorithm

The aim of this paper is to consider point pattern distributions over a network considering network spaces as structures for the distribution of point patterns. The term point pattern analysis indicates a set of methods used both in Spatial Analysis and Geographical Information Science to analyze the properties of distributions of points in a space. From a statistical point of view, an observed spatial point pattern can be thought as the outcome of a spatial stochastic process. Useful aspects of the behaviour of a general spatial stochastic process may be characterized by its first order properties, described in terms of the mean number of events per unit area at a certain point , and by its second order properties or spatial dependence which involve the relationship between numbers of event in pairs of subregions within R. In this paper we present an extension of the Kernel Density Estimation (KDE), called Point Pattern Network Density Estimation (PPNDE). Circular clusters of points distributed in the geographical space may be found by using Kernel Density Estimation; other configurations of cluster of points, depending on the network space, are also possible. In order to take into account this possibility the idea is to consider the kernel function as a density function based on network distances rather than on the Euclidean one. Some simulation experiments and an experiment based on a real data set end the paper.