Crime Prediction With Missing Data Via Spatiotemporal Regularized Tensor Decomposition

The goal of crime prediction is to forecast the number of crime incidents at each region of a city based on the historical crime data. It has attracted a great deal of attention from both academic and industrial communities due to its considerable significance in improving urban safety and reducing financial losses. Although much progress has been made in this field, most of the existing approaches assume that the historical crime data are complete, which does not hold in many real-world scenarios. Meanwhile, crime incidents are affected by multiple factors and have intricate spatial, temporal, and categorical correlations, which are not fully utilized by the current methods. In this article, we propose a novel tensor decomposition based framework, named TD-Crime, to conduct prediction directly on the incomplete crime data. Specifically, we first organize the crime data as a tensor and then apply the nonnegative CP decomposition to it, which not only provides a natural solution to the missing data problem but also captures the spatial, temporal, and categorical correlations implicitly. Moreover, we attempt to exploit the spatial and temporal correlations explicitly by directly learning from the crime data to further improve the forecasting performance. Finally, we obtain a joint optimization problem and present an efficient alternating optimization scheme to find a satisfactory solution. Extensive experiments on the real-world crime datasets show that TD-Crime can address the crime prediction task effectively under different missing data scenarios.