Permanent and transitory crime risk in variable-density hot spot analysis

TL;DR

The paper targets how crime hot spots evolve over two decades in Chicago using a variable-density clustering method that applies continuous distance matrix rescaling to address urban density heterogeneity. It combines hot spot analysis with cosmology-inspired two-point statistics to assess intra-cluster uniformity and crime-shape dynamics, revealing distinct cluster substructures and COVID-19–related shifts in crime composition. Key contributions include the first application of this rescaling to criminological data, identification of eight hot spots (with notable activity in the Chicago Loop), and an analysis of how area function modulates crime-type shares under pandemic conditions. The study highlights data-bias concerns in crime reporting and emphasizes the need for closer collaboration between operational research and policing practitioners to translate complex spatial analyses into actionable public safety strategies. Future work suggests temporal motion analyses and broader methodological integration to enhance patrol planning and resource allocation.

Abstract

Crime prevention measures, aiming for the effective and efficient spending of public resources, rely on the empirical analysis of spatial and temporal data for public safety outcomes. We perform a variable-density cluster analysis on crime incident reports in the City of Chicago for the years 2001--2022 to investigate changes in crime share composition for hot spots of different densities. Contributing to and going beyond the existing wealth of research on criminological applications in the operational research literature, we study the evolution of crime type shares in clusters over the course of two decades and demonstrate particularly notable impacts of the COVID-19 pandemic and its associated social contact avoidance measures, as well as a dependence of these effects on the primary function of city areas. Our results also indicate differences in the relative difficulty to address specific crime types, and an analysis of spatial autocorrelations further shows variations in incident uniformity between clusters and outlier areas at different distance radii. We discuss our findings in the context of the interplay between operational research and criminal justice, the practice of hot spot policing and public safety optimization, and the factors contributing to, and challenges and risks due to, data biases as an often neglected factor in criminological applications.

Figures (4)

• Figure 1: Descriptions of uniformity for crime distributions and types for the City of Chicago from 2001--2022. The upper two panels show Ripley's $F(d)$ and $G(d)$ functions in black, for a given distance $d$, with the median of Poisson simulations as a dashed line and their 95% confidence interval shaded. The lower eight panels depict the mean number of crimes per year across identified clusters in black, with darker and lighter shading indicating 95% and 68% confidence intervals for the different clusters, respectively.
• Figure 2: Clustering of Part I crime reports for the City of Chicago. The eight left-hand panels show the mean number of reports for different crime types, with the shaded regions indicating the 95% confidence intervals across types. The main right-hand panel depicts incidents falling within Clusters 1--8 with number flags, as well as non-cluster incidents in grey, with the subplot showing the agreement with a non-varying-density clustering.
• Figure 3: Cluster composition for crime reports in the City of Chicago from 2001--2022. The eight panels for separate Part I crimes show the evolution of the share of each cluster's total incidents that a given crime type contributes to that cluster over the years. The average of non-clustered outliers is shown as a solid black line.
• Figure 4: Spatial two-point autocorrelations for identified clusters in Part I crime incidents for the City of Chicago from 2001-2022, with shaded regions indicating 95% confidence intervals for multiple runs. The main panel shows correlations at different distance radii with a threshold of zero to alleviate the challenge of locations inaccessible for data collection, while the subplot depicts the non-thresholded correlations.