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Title: Internal cohesion and geometric shape of spatial clusters.
Authors: Duarte, Anderson Ribeiro
Duczmal, Luiz Henrique
Ferreira, Sabino José
Cançado, André Luiz Fernandes
Keywords: Kulldorff’s spatial scan statistics
Irregularly shaped clusters
Power tests
Compactness penalty function
Weak link internal cohesion
Issue Date: 2010
Citation: DUARTE, A. R. et al. Internal cohesion and geometric shape of spatial clusters. Environmental and Ecological Statistics, v. 17, n. 2, p. 203-229, jun. 2010. Disponível em: <>. Acesso em: 16 mar. 2017.
Abstract: The geographic delineation of irregularly shaped spatial clusters is an ill defined problem. Whenever the spatial scan statistic is used, some kind of penalty correction needs to be used to avoid clusters’ excessive irregularity and consequent reduction of power of detection. Geometric compactness and non-connectivity regularity functions have been recently proposed as corrections. We present a novel internal cohesion regularity function based on the graph topology to penalize the presence of weak links in candidate clusters. Weak links are defined as relatively unpopulated regions within a cluster, such that their removal disconnects it. By applying this weak link cohesion function, the most geographically meaningful clusters are sifted through the immense set of possible irregularly shaped candidate cluster solutions. A multiobjective genetic algorithm (MGA) has been proposed recently to compute the Paretosets of clusters solutions, employing Kulldorff’s spatial scan statistic and the geometric correction as objective functions. We propose novel MGAs to maximize the spatial scan, the cohesion function and the geometric function, or combinations of these functions. Numerical tests show that our proposed MGAs has high power to detect elongated clusters, and present good sensitivity and positive predictive value. The statistical significance of the clusters in the Pareto-set are estimated through Monte Carlo simulations. Our method distinguishes clearly those geographically inadequate clusters which are worse from both geometric and internal cohesion viewpoints. Besides, a certain degree of irregularity of shape is allowed provided that it does not impact internal cohesion. Our method has better power of detection for clusters satisfying those requirements. We propose a more robust definition of spatial cluster using these concepts.
ISSN: 1573-3009
Appears in Collections:DEEST - Artigos publicados em periódicos

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