Efficient regionalization techniques for socio‐economic geographical units using minimum spanning trees |
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| Authors: | R M AssunÇão M C Neves C Da Costa Freitas |
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| Institution: | 1. Federal University of Minas Gerais (UFMG) , Department of Statistics , Av. Ant?nio Carlos , 6627—Pampulha, 31270‐901, Belo Horizonte , MG , Brazil;2. Brazilian Agricultural Research Corporation (EMBRAPA) , Naticonal Centre for Environmental Monitoring (CNPMA) , 13820‐000 Jaguariúna , SP , Brazil;3. National Institute of Space Research (INPE) , Image Processing Division (DPI) , 12227‐001, S?o José dos Campos (SP) , Brazil |
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| Abstract: | Regionalization is a classification procedure applied to spatial objects with an areal representation, which groups them into homogeneous contiguous regions. This paper presents an efficient method for regionalization. The first step creates a connectivity graph that captures the neighbourhood relationship between the spatial objects. The cost of each edge in the graph is inversely proportional to the similarity between the regions it joins. We summarize the neighbourhood structure by a minimum spanning tree (MST), which is a connected tree with no circuits. We partition the MST by successive removal of edges that link dissimilar regions. The result is the division of the spatial objects into connected regions that have maximum internal homogeneity. Since the MST partitioning problem is NP‐hard, we propose a heuristic to speed up the tree partitioning significantly. Our results show that our proposed method combines performance and quality, and it is a good alternative to other regionalization methods found in the literature. |
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| Keywords: | Regionalization Constrained clustering Graph partitioning Optimization Zone design Census data analysis |
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