A Manifold Learning Data Enrichment Methodology for Homicide Prediction

Not all types of crime have the same priority in the agendas of policymakers since society tends to be more reluctant to more violent and costly crimes such as homicide. However, relative to other types of crime, homicides are statistically more challenging due to its sparsity and low frequency. For instance, over the last five years the average number of homicides across the city of Bogota has been roughly a thousand events per year, compared to the more than one hundred thousand robberies reported in the same period. Nevertheless, more than 80% of the homicides in the city occur during street fights suggesting a strong spatial and temporal correlation between these two types of crime. With this in mind, we used a manifold learning approach that capitalizes on a rich dataset of street fights to discover a criminal manifold that we use to penalize a KDE model of homicides where sparsity and low frequency is an issue. To implement this we follow a Kernel Warping methodology (Zhou & Matteson, 2015). The methodology reduces the relevant space for homicide prediction to regions of the city where homicides or street fights have occurred, giving more weight to the homicide episodes. We also introduce a temporal decay component to place a larger importance to recent events. The proposed model outperforms a standard KDE trained with homicide data, a KDE trained in both homicide and street fights data for homicide prediction, and a standard self-exciting point process on homicide data: flagging just the 5% of the area of the city with the highest estimated density, the Kernel Warping model correctly identifies between 30% and 35% of the homicides in the test set.11Results of the project “Diseno y validacion de modelos de analitica predictiva de fenomenos de seguridad y convivencia para la toma de decisiones en Bogota” funded by Colciencias with resources from the Sistema General de Regalias, BPIN 2016000100036. The opinions expressed are solely those of the authors.