Novel evaluation metrics for sparse spatio-temporal point process hotspot predictions - a crime case study

Many physical and sociological processes are represented as discrete events in time and space. These spatio-temporal point processes are often sparse, meaning that they cannot be aggregated and treated with conventional regression models. Models based on the point process framework may be employed instead for prediction purposes. Evaluating the predictive performance of these models poses a unique challenge, as the same sparseness prevents the use of popular measures such as the root mean squared error. Statistical likelihood is a valid alternative, but this does not measure absolute performance and is therefore difficult for practitioners and researchers to interpret. Motivated by this limitation, we develop a practical toolkit of evaluation metrics for spatio-temporal point process predictions. The metrics are based around the concept of hotspots, which represent areas of high point density. In addition to measuring predictive accuracy, our evaluation toolkit considers broader aspects of predictive performance, including a characterisation of the spatial and temporal distributions of predicted hotspots and a comparison of the complementarity of different prediction methods. We demonstrate the application of our evaluation metrics using a case study of crime prediction, comparing four varied prediction methods using crime data from two different locations and multiple crime types. The results highlight a previously unseen interplay between predictive accuracy and spatio-temporal dispersion of predicted hotspots. The new evaluation framework may be applied to compare multiple prediction methods in a variety of scenarios, yielding valuable new insight into the predictive performance of point process-based prediction

Determining the optimal spatial scan of Prospective space-time scan statistics (PSTSS) for crime hotspot prediction

The input value for the maximum spatial scan extent (K) of a prospective space-time scan statistical (PSTSS) technique is one important parameter that ensures accurate detection of the predictive hotspot of a geographical point events. Currently, there is no general consensus on how to determine the optimal value of K that maximises the predictive accuracy, especially in crime hotspot prediction. To address this issue, this study proposes a strategy in which different values of K are used to generate accuracy profiles that can be compared to determine optimal value of K. A case study presented shows that the best accuracy is obtained at K=250m, which is equivalent to the spatial aggregation of the crime dataset used. It is contended that this strategy could be extended to other geographical surveillance tasks

Graph deep learning model for network-based predictive hotspot mapping of sparse spatio-temporal events

The predictive hotspot mapping of sparse spatio-temporal events (e.g., crime and traffic accidents) aims to forecast areas or locations with higher average risk of event occurrence, which is important to offer insight for preventative strategies. Although a network-based structure can better capture the micro-level variation of spatio-temporal events, existing deep learning methods of sparse events forecasting are either based on area or grid units due to the data sparsity in both space and time, and the complex network topology. To overcome these challenges, this paper develops the first deep learning (DL) model for network-based predictive mapping of sparse spatio-temporal events. Leveraging a graph-based representation of the network-structured data, a gated localised diffusion network (GLDNet) is introduced, which integrating a gated network to model the temporal propagation and a novel localised diffusion network to model the spatial propagation confined by the network topology. To deal with the sparsity issue, we reformulate the research problem as an imbalance regression task and employ a weighted loss function to train the DL model. The framework is validated on a crime forecasting case of South Chicago, USA, which outperforms the state-of-the-art benchmark by 12% and 25% in terms of the mean hit rate at 10% and 20% coverage level, respectively

Scalable high-resolution forecasting of sparse spatiotemporal events with kernel methods: a winning solution to the NIJ "Real-Time Crime Forecasting Challenge"

We propose a generic spatiotemporal event forecasting method, which we developed for the National Institute of Justice’s (NIJ) RealTime Crime Forecasting Challenge (National Institute of Justice, 2017). Our method is a spatiotemporal forecasting model combining scalable randomized Reproducing Kernel Hilbert Space (RKHS) methods for approximating Gaussian processes with autoregressive smoothing kernels in a regularized supervised learning framework. While the smoothing kernels capture the two main approaches in current use in the field of crime forecasting, kernel density estimation (KDE) and self-exciting point process (SEPP) models, the RKHS component of the model can be understood as an approximation to the popular log-Gaussian Cox Process model. For inference, we discretize the spatiotemporal point pattern and learn a log-intensity function using the Poisson likelihood and highly efficient gradientbased optimization methods. Model hyperparameters including quality of RKHS approximation, spatial and temporal kernel lengthscales, number of autoregressive lags, bandwidths for smoothing kernels, as well as cell shape, size, and rotation, were learned using crossvalidation. Resulting predictions significantly exceeded baseline KDE estimates and SEPP models for sparse events

CPC: Crime, Policing and Citizenship - Intelligent Policing and Big Data

Crime, Policing and Citizenship (CPC) – Space-Time Interactions of Dynamic Networks has been a major UK EPSRC-funded research project. It has been a multidisciplinary collaboration of geoinformatics, crime science, computer science and geography within University College London (UCL), in partnership with the Metropolitan Police Service (MPS). The aim of the project has been to develop new methods and applications in space-time analytics and emergent network complexity, in order to uncover patterning and interactions in crime, policing and citizen perceptions. The work carried out throughout the project will help inform policing at a range of scales, from the local to the city-wide, with the goal of reducing both crime and the fear of crime. The CPC project is timely given the tremendous challenging facing policing in big cities nationally and globally, as consequences of changes in society, population structure and economic well-being. It addresses these issues through an intelligent approach to data-driven policing, using daily reported crime statistics, GPS traces of foot and vehicular patrols, surveys of public attitudes and geo-temporal demographic data of changing community structure. The analytic focus takes a spatio-temporal perspective, reflecting the strong spatial and temporal integration of criminal, policing and citizen activities. Street networks are used throughout as a basis for analysis, reflecting their role as a key determinant of urban structure and the substrate on which crime and policing take place. The project has presented a manifesto for ‘intelligent policing’ which embodies the key issues arising in the transition from Big Data into actionable insights. Police intelligence should go beyond current practice, incorporating not only the prediction of events, but also how to respond to them, and how to evaluate the actions taken. Cutting-edge network-based crime prediction methods have been developed to accurately predict crime risks at street segment level, helping police forces to focus resources in the right places at the right times. Methods and tools have been implemented to support senior offices in strategic planning, and to provide guidance to frontline officers in daily patrolling. To evaluate police performance, models and tools have been developed to aid identification of areas requiring greater attention, and to analyse the patrolling behaviours of officers. Methods to understand and model confidence in policing have also been explored, suggesting strategies by which confidence in the police can be improved in different population segments and neighbourhood areas. A number of tools have been developed during the course of the project include data-driven methods for crime prediction and for performance evaluation. We anticipate that these will ultimately be adopted in daily policing practice and will play an important role in the modernisation of policing. Furthermore, we believe that the approaches to the building of public trust and confidence that we suggest will contribute to the transformation and improvement of the relationship between the public and police

Investigating the impacts of training data set length (T) and the aggregation unit size (M) on the accuracy of the self-exciting point process (SEPP) hotspot method

This study examines the impacts of two variables; the training data lengths (T) and the aggregation unit sizes (M); on the accuracy of the self-exciting point process (SEPP) model during crime prediction. A case study of three crime types in the South Chicago area is presented, in which different combinations of values of T and M are used for 100 daily consecutive crime predictions. The results showed two important points regarding the SEPP model: first is that large values of T are likely to improve the accuracy of the SEPP model and second is that, a small aggregation unit, such as a 50m x 50m grid, is better in terms of capturing local repeat and near-repeat patterns of crimes