Multi-instance learning with application to the profiling of multi-victim homicides

Abstract

Homicide involving multiple victims has a significant negative effect on society. Criminal profiling consists of determining the traits of an unknown offender based on those of the crime and the victims, with a view to their identification. To provide the most likely profile of the perpetrator of a multi-victim homicide, we propose a predictive model of supervised machine learning based on a Bayesian Network. Conventional classifiers can generate the perpetrator’s profile according to the traits of each of the victims of the same homicide, but the profiles may differ from one another. To address this issue, we consider the Multi-Instance (MI) learning framework, in which the victims of the same incident form a bag, and each bag is associated with a unique label for each of the perpetrator’s features. We introduce the unanimity MI assumption in this domain, and accordingly allocate a label to the bag based on the labels and probabilities the Bayesian Network has assigned its instances, using a combination rule from those of the ensemble of classifiers. We apply this methodology to the Federal Bureau of Investigation (FBI) homicide database to compare three combination rules empirically in the validation process, as well as theoretically, using the one that ultimately proves to be the best to build the final model, which is then applied in some illustrative examples to achieve the criminal profile.