Spatial Cluster Detection Through a Dynamic Programming Approach

  • Gladston J. P. Moreira
  • Luís Paquete
  • Luiz H. Duczmal
  • David Menotti
  • Ricardo H. C. Takahashi
Living reference work entry

Abstract

This chapter reviews a dynamic programming scan approach to the detection and inference of arbitrarily shaped spatial clusters in aggregated geographical area maps, which is formulated here as a classic knapsack problem. A polynomial algorithm based on constrained dynamic programming is proposed, the spatial clusters detection dynamic scan. It minimizes a bi-objective vector function, finding a collection of Pareto optimal solutions. The dynamic programming algorithm is adapted to consider geographical proximity between areas, thus allowing a disconnected subset of aggregated areas to be included in the efficient solutions set. It is shown that the collection of efficient solutions generated by this approach contains all the solutions maximizing the spatial scan statistic. The plurality of the efficient solutions set is potentially useful to analyze variations of the most likely cluster and to investigate covariates.

Keywords

Spatial scan statistic Irregular clusters Dynamic programming Multi-objective optimization 

References

  1. Beier R, Röglin H, Vöcking B (2007) The smoothed number of pareto optimal solutions in bicriteria integer optimization. In: Integer programming and combinatorial optimization. Lecture notes in computer science, vol 4513. Springer, Berlin/Heidelberg, pp 53–67Google Scholar
  2. Duczmal L, Kulldorff M, Huang, L (2006) Evaluation of spatial scan statistics for irregularly shaped disease clusters. J Comput Graph Stat 15:428–442CrossRefGoogle Scholar
  3. Ehrgott M (2000) Multicriteria optimization. Springer, Berlin/New YorkCrossRefMATHGoogle Scholar
  4. Kulldorff M (1997) A spatial scan statistic. Commun Stat Theory Methods 26:1481–1496MathSciNetCrossRefMATHGoogle Scholar
  5. Kulldorff M (1999) Spatial scan statistics: models, calculations and applications. In: Glaz B (ed) Scan statistics and applications. Boston, Birkhauser, pp 303–322CrossRefGoogle Scholar
  6. Moreira GJP, Paquete L, Duczmal L, Menotti D, Takahashi RHC (2015) Multi-objective dynamic programming for spatial cluster detection. Environ Ecol Stat 22(2):369–391MathSciNetCrossRefGoogle Scholar
  7. Neill DB (2012) Fast subset scan for spatial pattern detection. J R Stat Soc Ser B 74:337–360MathSciNetCrossRefGoogle Scholar
  8. Nemhauser GL, Ullmann Z (1969) Discrete dynamic programming and capital allocation. Manag Sci 15(9):494–505MathSciNetCrossRefMATHGoogle Scholar
  9. Oliveira F, Duczmal L, Cancado A, Tavares R (2011) Nonparametric intensity bounds for the delineation of spatial clusters. Int J Health Geogr 10(1):1CrossRefGoogle Scholar
  10. Paquete L, Jaschob M, Klamroth K, Gorski J (2013) On a biobjective search problem in a line: formulations and algorithms. Theor Comput Sci 507(0):61–71MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media LLC 2017

Authors and Affiliations

  • Gladston J. P. Moreira
    • 1
  • Luís Paquete
    • 2
  • Luiz H. Duczmal
    • 3
  • David Menotti
    • 4
  • Ricardo H. C. Takahashi
    • 5
  1. 1.Department of ComputingUniversidade Federal de Ouro PretoOuro PretoBrazil
  2. 2.CISUC, Department of Informatics EngineeringUniversity of CoimbraLisbonPortugal
  3. 3.Department of StatisticsUniversidade Federal de Minas GeraisBelo HorizonteBrazil
  4. 4.Department of InformaticsUniversidade Federal do ParanáCuritibaBrazil
  5. 5.Department of MathematicsUniversidade Federal de Minas GeraisBelo HorizonteBrazil

Section editors and affiliations

  • Joseph Glaz
    • 1
  • Markos V. Koutras
    • 2
  1. 1.Department of StatisticsUniversity of ConnecticutStorrsUSA
  2. 2.Dept. of Statistics and Insurance Science, University of PiraeusPiraeusGreece

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