Fuzzy-Based Spatiotemporal Hot Spot Intensity and Propagation—An Application in Crime Analysis

Cluster-based hot spot detection is applied in many disciplines to analyze the locations, concentrations, and evolution over time for a phenomenon occurring in an area of study. The hot spots consist of areas within which the phenomenon is most present; by detecting and monitoring the presence of hot spots in different time steps, it is possible to study their evolution over time. One of the most prominent problems in hot spot analysis occurs when measuring the intensity of a phenomenon in terms of the presence and impact on an area of study and evaluating its evolution over time. In this research, we propose a hot spot analysis method based on a fuzzy cluster hot spot detection algorithm, which allows us to measure the incidence of hot spots in the area of study. We analyze its variation over time, and in order to evaluate its reliability we use a well-known fuzzy entropy measure that was recently applied to measure the reliability of hot spots by executing fuzzy clustering algorithms. We apply this method in crime analysis of the urban area of the City of London, using a dataset of criminal events that have occurred since 2011, published by the City of London Police. The obtained results show a decrease in the frequency of all types of criminal events over the entire area of study in recent years.