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Spatial Cluster Detection Through a Dynamic Programming Approach

In: Handbook of Scan Statistics

Author

Listed:
  • Gladston J. P. Moreira

    (Universidade Federal de Ouro Preto, Department of Computing)

  • Luís Paquete

    (University of Coimbra, CISUC, Department of Informatics Engineering)

  • Luiz H. Duczmal

    (Universidade Federal de Minas Gerais, Campus Pampulha, Department of Statistics)

  • David Menotti

    (Universidade Federal do Paraná, Department of Informatics)

  • Ricardo H. C. Takahashi

    (Universidade Federal de Minas Gerais, Department of Mathematics)

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.

Suggested Citation

  • Gladston J. P. Moreira & Luís Paquete & Luiz H. Duczmal & David Menotti & Ricardo H. C. Takahashi, 2024. "Spatial Cluster Detection Through a Dynamic Programming Approach," Springer Books, in: Joseph Glaz & Markos V. Koutras (ed.), Handbook of Scan Statistics, chapter 30, pages 595-608, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-8033-4_40
    DOI: 10.1007/978-1-4614-8033-4_40
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