期刊
出版社
ROYAL SOC
DOI: 10.1098/rsta.2013.0403
关键词
crime hotspots; density estimation; graph Laplacian; maximum penalized likelihood estimation; non-local means; Nystrom's extension
资金
- NSF [DMS-0968309, DMS-1417674, DGE-1144087]
- W.M. Keck Foundation
- ONR [N000141210040, N000141210838]
- AFOSR MURI [FA9550-10-1-0569]
- ARO [W911NF1010472]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0968309, 1417674] Funding Source: National Science Foundation
Given a discrete sample of event locations, we wish to produce a probability density that models the relative probability of events occurring in a spatial domain. Standard density estimation techniques do not incorporate priors informed by spatial data. Such methods can result in assigning significant positive probability to locations where events cannot realistically occur. In particular, when modelling residential burglaries, standard density estimation can predict residential burglaries occurring where there are no residences. Incorporating the spatial data can inform the valid region for the density. When modelling very few events, additional priors can help to correctly fill in the gaps. Learning and enforcing correlation between spatial data and event data can yield better estimates from fewer events. We propose a non-local version of maximum penalized likelihood estimation based on the H-1 Sobolev seminorm regularizer that computes non-local weights from spatial data to obtain more spatially accurate density estimates. We evaluate this method in application to a residential burglary dataset from San Fernando Valley with the non-local weights informed by housing data or a satellite image.
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