Disentangle crime hot spots and displacements in space and time: An analysis for Chicago from 2001 to 2016

Violence and crime have been regarded as one of the notorious behaviors against humanity. With the rapid development of Information and Communications Technology (ICT), increasing amount of crime data become much more available and useful not only for police dispatch and crime prevention, but also for providing important references for the personal safety of local residents and visitors, especially in large cities. In this paper, we apply statistical approaches and graph theory to characterize the spatiotemporal properties of Chicago crime data from 2001 to 2016. First, we improved the previous Space-Time Kernel Density Estimation (STKDE) methods in computational efficiency. We proved that our improved method to compute STKDE has linear time computational complexity, which is experimentally verified to be much faster than previous methods. Second, we applied our improved STKDE method to demonstrate the intensities and hot spots of crime distribution in Chicago from 2001 to 2016. In order to reveal the displacement of crime incidents (i.e. movements of the hot spots), we detected the locations of highest crime hot spots at specified time intervals, and created hot spot displacement graphs based on whether a geographic location continues to be a crime hot spot across time intervals. Finally, the method of longest path on Directed Acyclic Graphs (DAG) was applied on the hot spot displacement graph in addition to the analysis of the number of components and their sizes of the graph. The result showed spatial crime displacement and temporal crime duration patterns. The proposed method advanced our knowledge in digital humanities, which can be applied to other cities, providing useful information for public safety.