Internal cohesion and geometric shape of spatial clusters |
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Authors: | Anderson Ribeiro Duarte Luiz Duczmal Sabino José Ferreira André Luiz F Cançado |
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Institution: | (1) Statistics Department, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil;(2) Department of Mathematics, Universidade Federal de Ouro Preto, Ouro Preto, Brazil; |
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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 multi-objective genetic algorithm (MGA) has
been proposed recently to compute the Pareto-sets 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. |
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