Local indicators of network-constrained clusters in spatial point patterns

The detection of clustering in a spatial phenomenon of interest is an important issue in spatial pattern analysis. While traditional methods mostly rely on the planar space assumption, many spatial phenomena defy the logic of this assumption. For instance, certain spatial phenomena related to human activities are inherently constrained by a transportation network because of our strong dependence on the transportation system. This article thus introduces an exploratory spatial data analysis method named local indicators of network-constrained clusters (LINCS), for detecting local-scale clustering in a spatial phenomenon that is constrained by a network space. The LINCS method presented here applies to a set of point events distributed over the network space. It is based on the network K-function, which is designed to determine whether an event distribution has a significant clustering tendency with respect to the network space. First, an incremental K-function is developed so as to identify cluster size more explicitly than the original K-function does. Second, to enable identification of cluster locations, a local K-function is derived by decomposing and modifying the original network K-function. The local K-function LINCS, which is referred to as KLINCS, is tested on the distribution of 1997 highway vehicle crashes in the Buffalo, NY area. Also discussed is an adjustment of the KLINCS method for the nonuniformity of the population at risk over the network. As traffic volume can be seen as a surrogate of the population exposed to a risk of vehicle crashes, the spatial distribution of vehicle crashes is examined in relation to that of traffic volumes on the network. The results of the KLINCS analysis are validated through a comparison with priority investigation locations (PILs) designated by the New York State Department of Transportation.