A study of K-functions at different levels of detail of network data

Abstract

Spatial data are created at different levels of detail (LOD), for example, a road network is sometimes represented only by intercity roads or sometimes by both intercity and intracity roads. This difference in LOD causes a problem because it affects spatial analysis. This paper deals with this LOD-dependent problem, specifically focusing on network K-function analysis, which is frequently conducted for interpreting point patterns. First, a mathematical model is developed based on a simple radial network. From this mathematical model, it is explicitly found that the lowest limit, K̄low (h), of estimated K-values exists independently from the LOD of network data. Second, to extend the considerations into K-functions to actually observed networks, road network data are considered in which K-values are computed using Monte Carlo simulation. The obtained K-values imply that the lowest limit, K̄low (h), also exists in networks in the real world. This result suggests that spatial analysts are empirically, in some cases, able to interpret point patterns without taking into account the LOD of network data.