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A computationally efficient method for delineating irregularly shaped spatial clusters

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Abstract

In this paper, we present an efficiency improvement for the algorithm called AMOEBA, A Multidirectional Optimum Ecotope-Based Algorithm, devised by Aldstadt and Getis (Geogr Anal 38(4):327–343, 2006). AMOEBA embeds a local spatial autocorrelation statistic in an iterative procedure in order to identify spatial clusters (ecotopes) of related spatial units. We provide an analysis of the computational complexity of the original AMOEBA and develop an alternative formulation that reduces computational time without losing optimality. Empirical evidence is provided using georeferenced socio-demographic data in Accra, Ghana.

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Notes

  1. A collection of statistical tests for cluster detection is available in a software package named GeoSurveillance. See Yamada et al. (2009) for more information about this software.

  2. In general, the problem of spatial clustering is related to a family of problems that are classified as N-P hard (Wu et al. 2007; Gaudart et al. 2005). The combinatorial complexity of this type of problems has led researchers to primarily focus on the development of algorithmic solutions.

  3. The power set of a set M is the set of all subsets of M.

  4. Other options to generate different spatial clustering patterns, like the spiral or linear clustering pattern, can be found in Jackson et al. (2010).

  5. NumPy provides a wide variety of mathematical functions needed for scientific computing with Python (Oliphant 2006).

  6. The algorithm as a Python module is also available from the authors on request.

  7. For each instance we generated 1,000 random permutations to perform the Monte Carlo-type permutation test.

  8. This is because the percentage of areas that are assigned to be part of clusters is fixed, which implies that a larger number of clusters results in smaller cluster size.

  9. http://geography.sdsu.edu/Research/Projects/IPC/ipc2research.html.

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Acknowledgments

The authors thank Professor Dr. John Weeks, director of the International Population Center at San Diego State University, for providing us with the data for our empirical application. The usual disclaimer applies.

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Authors and Affiliations

  1. Research in Spatial Economics (RISE-group), Department of Economics, EAFIT University, Carrera 49 7 Sur-50, Medellin, Colombia

    Juan C. Duque

  2. Department of Geography, University at Buffalo, 117 Wilkeson Quad, Buffalo, NY, 14261-0055, USA

    Jared Aldstadt

  3. Research in Spatial Economics (RISE-group), Department of Fundamental Sciences, EAFIT University, Carrera 49 7 Sur-50, Medellin, Colombia

    Ermilson Velasquez, Jose L. Franco & Alejandro Betancourt

Authors
  1. Juan C. Duque
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  2. Jared Aldstadt
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  3. Ermilson Velasquez
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  4. Jose L. Franco
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  5. Alejandro Betancourt
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Correspondence to Juan C. Duque.

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Duque, J.C., Aldstadt, J., Velasquez, E. et al. A computationally efficient method for delineating irregularly shaped spatial clusters. J Geogr Syst 13, 355–372 (2011). https://doi.org/10.1007/s10109-010-0137-1

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  • DOI: https://doi.org/10.1007/s10109-010-0137-1

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