Modeling and prediction of criminal activity based on spatio-temporal probabilistic risk functions

Abstract

Security forces need to model risk patterns associated with criminal activity to study cause-effect relationships and predict new crimes. In this regard, criminal risk models are important to obtain relevant information for better resource allocation and prevention of future crime activity. This paper proposes a method to model and predict future criminal activity based on spatial probabilistic risk functions and a characterization of their temporal evolution as new data become available. This method uses geo-referenced information of public services (e.g., shopping centers, banks) and criminal incidents to approximate the prior risk function as a Gaussian Mixture Model (GMM). Temporal evolution of crime activity is characterized using an algorithm that is based on Sequential Monte Carlo Methods and Importance Sampling. This algorithm incorporates information from new measurements, in a recursive manner, to approximate the posterior spatial probabilistic risk function by updating particle positions in the map. Finally, we propose a novel prediction scheme for criminal activity that uses Gaussian fields centered on hypothetical future criminal events, which are sampled from a GMM that characterizes the spatial distribution associated with recent crime activity. The optimum number of centroids for each Gaussian kernel is evaluated using Silhouette algorithm. The time index related to each hypothetical future crime event is probabilistically characterized using an exponential distribution. Results using real data show that the majority of future events occur within risk modeled zones, information which can be used for resource allocation and improvement of intervention plans.