  Crimes emerge out of complex interactions of human behaviors and situations.
Linkages between crime incidents are highly complex. Detecting crime linkage
given a set of incidents is a highly challenging task since we only have
limited information, including text descriptions, incident times, and
locations. In practice, there are very few labels. We propose a new statistical
modeling framework for {\it spatio-temporal-textual} data and demonstrate its
usage on crime linkage detection. We capture linkages of crime incidents via
multivariate marked spatio-temporal Hawkes processes and treat embedding
vectors of the free-text as {\it marks} of the incident, inspired by the notion
of {\it modus operandi} (M.O.) in crime analysis. Numerical results using real
data demonstrate the good performance of our method as well as reveals
interesting patterns in the crime data: the joint modeling of space, time, and
text information enhances crime linkage detection compared with the
state-of-the-art, and the learned spatial dependence from data can be useful
for police operations.
