On the application of fuzzy clustering for crime hot spot detection

One of the fundamental challenges in crime mapping and analysis is pattern recognition. Efforts and methods to detect crime hot-spots, or geographic areas of elevated criminal activity, are wide ranging. For aggregate data, such as total crime events in a census tract(s). measures of spatial autocorrelation have proven useful. For disaggregate data (i.e. individual crime events), kernel density smoothing and non-hierarchical cluster analysis (e.g. k-means), are widely used. Non-hierarchical techniques are particularly effective in delineating geographic space into areas of higher or lower crime concentrations, because each observation is assigned to one and only one cluster. The resulting set of partitions provides clear-cut spatial boundaries that can be used for hot-spot evaluation and interpretation. However, the strength of non-hierarchical methods can also be viewed as a weakness. Although the hard-clustering of observations into a set of discrete clusters is helpful, there are many cases where ambiguity exists in the data. In such cases, a more generalized approach for hot-spot detection would be helpful. The purpose of this paper is to explore the use of a generalized partitioning method known as fuzzy clustering for hot-spot detection. Functional and visual comparisons of fuzzy clustering and two hard-clustering approaches (medoid and A'-means), across a range of cluster values are analyzed. The empirical results suggest that a fuzzy clustering approach is better equipped to handle intermediate cases and spatial outliers.