How is the confidentiality of crime locations affected by parameters in kernel density estimation?

Abstract

Kernel density estimation (KDE) is widely adopted to show the overall crime distribution and at the same time obscure exact crime locations due to the confidentiality of crime data in many countries. However, the confidential level of crime locational information in the KDE map has not been systematically investigated. This study aims to examine whether a kernel density map could be reverse-transformed to its original map with discrete crime locations. Using the Epanecknikov kernel function, a default setting in ArcGIS for density mapping, the transformation from a density map to a point map was conducted with various combinations of parameters to examine its impact on the deconvolution process (density to point location). Results indicate that if the bandwidth parameter (search radius) in the original convolution process (point to density) was known, the original point map could be fully recovered by a deconvolution process. Conversely, when the parameter was unknown, the deconvolution process would be unable to restore the original point map. Experiments on four different point maps—a random point distribution, a simulated monocentric point distribution, a simulated polycentric point distribution, and a real crime location map—show consistent results. Therefore, it can be concluded that the point location of crime events cannot be restored from crime density maps as long as parameters such as the search radius parameter in the density mapping process remain confidential.