  Our goal is to predict the location of the next crime in a crime series,
based on the identified previous offenses in the series. We build a predictive
model called Next Hit Predictor (NHP) that finds the most likely location of
the next serial crime via a carefully designed risk model. The risk model
follows the paradigm of a self-exciting point process which consists of a
background crime risk and triggered risks stimulated by previous offenses in
the series. Thus, NHP creates a risk map for a crime series at hand. To train
the risk model, we formulate a convex learning objective that considers
pairwise rankings of locations and use stochastic gradient descent to learn the
optimal parameters. Next Hit Predictor incorporates both spatial-temporal
features and geographical characteristics of prior crime locations in the
series. Next Hit Predictor has demonstrated promising results on decades' worth
of serial crime data collected by the Crime Analysis Unit of the Cambridge
Police Department in Massachusetts, USA.
