Spatio-Temporal Forecasting of Crime: Application of Classical and Neural Network Methods

This paper introduces a new spatio-temporal forecasting methodology that combines artificial neural networks and cellular automata with GIS-based data. The technique, which we refer to as chaotic cellular forecasting (CCF) is similar to spatial adaptive filtering due to Foster and Gorr (1986) and weighted spatial adaptive filtering due to Gorr and Olligschlaeger (1994) in that it uses contiguity relationships and the geographer’s assumption that influence between data points decays with distance. As with spatial adaptive filtering the methodology uses an iterative process to arrive at a solution. Unlike spatial adaptive filtering, however, chaotic forecasting uses a gradient descent method rather than a grid search to find the optimal set of parameters (or, in the case of artificial neural networks, weights). In addition, and most importantly, CCF has the nonlinear and multi-model functional form commonly used in neural net modeling, allowing for increased pattern recognition and accommodation of spatio-temporal heterogeneity. The result is a robust spatio-temporal forecasting method that requires very little model specification, is self - adaptive and performs very well on data sets that exhibit non-traditional statistical behavior.