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Title

MESH MODELING FOR SPATIALLY ADAPTIVE DENSITY MAPPING OF CRIME DATA

Creator

Ramon, Albert Juan

Date

2015, 2015-05

Description

As computing technology has become an essential tool for law enforcement, crime mapping has evolved from the use of pushpins on paper maps to...
Show moreAs computing technology has become an essential tool for law enforcement, crime mapping has evolved from the use of pushpins on paper maps to the use of computerized geographical information systems (GIS). The use of GIS permits real-time display of maps showing crime “hotspots,” facilitating the implementation of specific crime prevention strategies targeting the affected locations. Until recently, crime maps merely presented a summary of previous crime incidents; however, as part of a new concept called “predictive policing”, efforts are now underway to produce crime maps that are predictive, highlighting geographical regions that an algorithm determines are likely to experience abnormally high (or low) crime levels in the near future. Traditionally, crime maps are produced by representing crime data (a spatiotemporal point process) on a uniform grid, similar to the way in which pixels are used to represent digital images. However, the problem of predictive policing places new demands on mapping, raising questions about how maps should ideally be made. For example, there is considerable uncertainty concerning how best to optimize the grid spacing in a predictive map: If the pixels are too small, the past data required to predict future crime will be too sparse to enable good prediction performance; if the pixels are too large, each prediction will cover too large of a geographical region, the behavior of crime within the region may be heterogeneous and not well captured by a single predictive model, and coarse-scale predictions will not be sufficiently specific to be acted upon by police. In this thesis, a novel method for representing crime mapping data is proposed, in which the conventional pixel representation is replaced by a non-uniform sampling scheme based on mesh modeling, an approach that was first proposed in the context of image processing by members of our research group. In the present context, the goal is to adapt the spatial sampling to the local density of available training data in an effort to equalize prediction performance across a predictive map while accurately representing the spatial density. Geographical areas having few crimes will be represented more coarsely by this approach, with high-crime areas being represented at a fine spatial scale. We used various metrics to test the proposed approaches based on real and simulated crime-incident data for the City of Chicago. The results of our experiments demonstrate that the proposed method is a promising framework for predictive crime mapping. In future work, our hypothesis about the value of spatial sampling adaptation will be tested through the use of the proposed method within a complete spatio-temporal prediction algorithm. Although this thesis focuses only on representation of crime data, we anticipate that the proposed method may find application in other density estimation or mapping problems in which smooth densities are to be approximated from spatial point-process data.
M.S. in Electrical Engineering, May 2015
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