Content area
Full Text
Abstract
Hot-spot maps are used by a majority of police departments throughout the United States. These maps are used to determine policing decisions such as community resource allocation and police presence. There are various methods to generate these maps; however, there is no consensus on when each specific mapping technique is best to use. We argue this is due to a lack of understanding of how "good" a hot-spot map is relative to another. Many data scientists use statistical metrics to evaluate hot-spot maps, while many police departments and hot-spot software use indices developed in the criminology literature. This paper bridges the gap between these fields by advancing the mathematical understanding of recent criminology hot-spot indices. We create a standard mathematical notation for hot-spot indices and explore the mathematical intuition and knapsack problem inherent in evaluating the most recent index, the Prediction Efficiency Index· (PEI·). We conclude with some directions where the evaluation of hot-spot maps might go in the future.
Keywords Hot-spot mapping; knapsack application; criminal justice; spatiotemporal metrics
1. Introduction
Most police departments use hot-spot maps to identify crime patterns [1]. These crime hot-spot maps are used to allocate resources within various types of policing efforts, such as problem-orientated policing (e.g., enhancing location characteristics), community-oriented policing (e.g., improving community dynamics), and traditional policing activities (e.g., increasing or concentrating police presence) [2]. There are various methods to create these crime hot-spot maps, from naive models to advanced machine learning algorithms. However, the literature is conflicting as to which model is the best; some argue Random Forest (RP), Kernel-Density Estimation (KDE), Multilayer Perceptron (MLP), and Risk Terrain Modeling (RTM) are among the most promising methods [3, 4]. A lack of consistent terminology, evaluation criteria, and reporting of initial parameters are some reasons behind the lack of consensus [3]. Since crime hot-spot maps have become central to various police and community resources decisions, it is critical to clearly communicate the metrics used to evaluate and compare maps. We begin by summarizing the two separate research directions in developing metrics to evaluate hot-spot maps: statistical metrics used in machine learning and computer science literature and crime indices used by police and criminologists. We then recontextualize current criminal justice crime indices into a consistent mathematical notation. Lastly,...