Identifying high risk crime areas using topology

Computational criminology is an area of research that joins advanced theories in criminology with theories and methods in mathematics, computing science, geography and behavioural psychology. It is a multidisciplinary approach that takes the strengths of several disciplines and, with semantic challenges, builds new methods for the analysis of crime and crime patterns. This paper presents a developing algorithm for linking the geographic and cognitive psychology sides of criminology research with a prototype topology algorithm that joins local urban areas together using rules that define similarity between adjacent small units of analysis. The approach produces irregular shapes when mapped in a Euclidean space, but which follow expectations in a non-Euclidean topological sense. There are high local concentrations or hot spots of crime but frequently there is a sharp break on one side of the hot spot and with a gradual diffusion on the other. These shapes follow the cognitive psychological way of moving from one location to another without noticing gradual changes or conversely being aware of sharp changes from one location to the next. This article presents a pattern modeling approach that uses topology to spatially identify the concentrations of crime and their crisp breaks and gradual blending into adjacent areas using the basic components: interior, boundary and exterior. This topology algorithm is used to analyze crimes in a moderate sized city in British Columbia.