Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
G Soete ParticleDe (1987) ArticleTitleLeast squares algorithms for constructing constrained ultrametric and additive tree representations of symmetric proximity data J Classifica 4 155–173 Occurrence Handle10.1007/BF01896984
BoundarySeer (2005) Software for geographic boundary analysis. TerraSeer Ann Arbor MI
Everitt B, Landau S, Leese M (2001) Cluster analysis. Arnold, London, pp 161–164
M Kulldorff N Nagarwalla (1995) ArticleTitleSpatial disease clusters: detection and inference Statistics in Medicine 14 799–810 Occurrence Handle7644860 Occurrence Handle1:STN:280:ByqA2s3nsFY%3D
L Lebart (1978) ArticleTitleProgramme d’agrégation avec constraints (C.A.H. contiguïté) Cah Anal Donnée 3 275–287
P Legendre (1987) Constrained clustering L Legendre (Eds) Developments in numerical ecology Springer-Verlag Berlin 289–307
P Legendre L Legendre (1998) Numerical ecology Elsevier NY 853
P Legendre K Ellingsen E Bjornbom P Casgrain (2002) ArticleTitleAcoustic seabed classification: improved statistical method Can J Fish Aqua Sci 59 IssueID7 1085–1089 Occurrence Handle10.1139/f02-096
Legendre P, Vaudor A, Casgrain P (2005) The R package for spatial and multidimensional analysis. Software available at http://www.bio.umontreal.ca/Casgrain/en/labo/index.html
Modarres R, Patil GP (2006) Hotspot Detection with Bivariate Data. To appear in the J Stat Plan Infer
GP Patil C Taillie (2004) ArticleTitleUpper level set scan statistic for detecting arbitrarily shaped hotspots Environ Ecol Stat 11 183–197 Occurrence Handle10.1023/B:EEST.0000027208.48919.7e
Urban DL (2004) Multivariate Analysis. Nonhierarchical Agglomeration. Spatially Constrained Classification. http://www.env.duke.edu/landscape/classes/env358/mv_pooling.pdf
Author information
Authors and Affiliations
Corresponding author
Additional information
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.
Rights and permissions
About this article
Cite this article
Patil, G.P., Modarres, R., Myers, W.L. et al. Spatially constrained clustering and upper level set scan hotspot detection in surveillance geoinformatics. Environ Ecol Stat 13, 365–377 (2006). https://doi.org/10.1007/s10651-006-0017-5
Issue Date:
DOI: https://doi.org/10.1007/s10651-006-0017-5