title: Non-local crime density estimation incorporating housing information.
abstract: 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.
authors.affiliation: Department of Mathematics, University of California, Los Angeles, CA 90095, USA jwoodworth@math.ucla.edu.
authors.forename: J T
authors.initials: JT
authors.lastname: Woodworth
authors.affiliation: Department of Mathematics and Computer Science, Santa Clara University, Santa Clara, CA 95053-0290, USA.
authors.forename: G O
authors.initials: GO
authors.lastname: Mohler
authors.affiliation: Department of Mathematics, University of California, Los Angeles, CA 90095, USA.
authors.forename: A L
authors.identifier: http://orcid.org/0000-0003-0396-7391
authors.initials: AL
authors.lastname: Bertozzi
authors.affiliation: Department of Anthropology, University of California, Los Angeles, CA 90095, USA.
authors.forename: P J
authors.initials: PJ
authors.lastname: Brantingham
keywords: Nyström's extension; crime hotspots; density estimation; graph Laplacian; maximum penalized likelihood estimation; non-local means