Spatially constrained clustering and upper level set scan hotspot detection in surveillance geoinformatics

We discuss upper level set (ULS) scan as a type of spatially constrained clustering in relation to two ways of imposing the spatial constraint, retrospectively versus progressively. We show that ULS scan produces the same results both ways; whereas two popular clustering techniques, single-linkage and K-means, can yield different results when spatial constraints are imposed retrospectively versus progressively. The ULS scan approach examines spatially connected components of a tessellation as a threshold is moved from the highest level (value) in the data to the lowest level. When the variable of interest on the tessellation is a rate of incidence, then a significance test is available based on binomial or Poisson null models and Monte Carlo techniques. This is a common context for detecting hotspots of diseases in epidemiological work. We also discuss an approach for extending the univariate methodology to accommodate multivariate contexts. Received: September 2005 / Revised: February 2006 This material is based upon work supported by (i) the National Science Foundation under Grant No. 0307010, (ii) the United States Environmental Protection Agency under Grant No. CR-83059301 and (iii) the Pennsylvania Department of Health using Tobacco Settlement Funds under Grant No. ME 01324. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the agencies.