On Predicting Crime with Heterogeneous Spatial Patterns - Methods and Evaluation.

Accurate prediction of crime incidents can assist the police in better planning of prevention strategies and scheduling deployment. The problem is often studied as a spatio-temporal regression problem approached by dividing the area of interest into a grid of uniform cells, and performing regression on timeseries of each cell. We propose that changing the method of division of the area can significantly improve crime prediction. We demonstrate this using a heterogeneous division of the area obtained by our partitioning algorithm that takes into account the density of crime. We further show that existing measures do not provide a fair comparison of two methods that partition the area in two different ways. To address this severe drawback in crime prediction evaluation, we propose a novel measure which is based on optimal allocation of resources relying on the prediction and then checking the actual number of crimes that would have been avoided by the allocation. Essentially, our measure answers the question of which model would have assisted in preventing most number of actual crimes if allocation were to be done using the predicted crimes. We also prove that a greedy algorithm results in the optimal allocation resources, thus making our evaluation computationally lightweight. Experiments on real-world datasets demonstrate that heterogeneous division of the area results in improved crime prediction while drastically decreasing the number of models to be trained compared to uniform grid division.