Network density estimation: Analysis of point patterns over a network

Abstract

This research focuses on examining point pattern distributions over a network, therefore abandoning the usual hypotheses of homogeneity and isotropy of space and considering network spaces as frameworks for the distribution of point patterns. Many human related point phenomena are distributed over a space that is usually not homogenous and that depend on a network-led configuration. Kernel Density Estimation (KDE) and K-functions are commonly used and allow analysis of first and second order properties of point phenomena. Here an extension of KDE, called Network Density Estimation (NDE) is proposed. The idea is to consider the kernel as a density function based on network distances rather than Euclidean ones. That should allow identification of 'linear' clusters along networks and the identification of a more precise surface pattern of network related phenomena. © Springer-Verlag Berlin Heidelberg 2005.