Linear hotspot detection for a point pattern in the vicinity of a linear network

The analysis of point patterns on linear networks is receiving current attention in spatial statistics. This refers to the analysis of points in a spatial domain that coincide with a linear network like a road network. The linear network is modelled as a set of lines that are connected at their ends or are intersecting, that is, modelled as mathematical graphs. Limited research so far has been conducted on spatial points that fall on the Euclidean space containing the linear network. This study addresses new steps by exploring points in the vicinity of the network that do not necessarily fall on the linear network. We present a novel method that is motivated by crime locations amongst a road network. The aim is to detect spatial hotspots around a linear network, where crime locations are considered as a point pattern lying in the vicinity of the linear road network. A new connectivity measure is also introduced to define the line segment neighbours of a line segment. The methodology is applied to crime data in Khayelitsha, South Africa. We detect a pattern of crime locations within the network that can be well interpreted. We conclude that our method is well applicable and could potentially help governmental organisations to allocate measures to reduce criminality.