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Clusterização Hierárquica Espacial

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  • Alexandre Xavier Ywata Carvalho
  • Pedro Henrique Melo Albuquerque
  • Gilberto Rezende de Almeida Junior
  • Rafael Dantas Guimarães

Abstract

Este estudo apresenta uma nova metodologia para clusterização hierárquica espacial de polígonos contíguos, com base em um sistema de coordenadas georreferenciadas. O algoritmo proposto é construído a partir de uma modificação do algoritmo de clusterização hierárquica tradicional, comumente utilizado na literatura de análise multivariada. De acordo com o método proposto neste trabalho, a cada passo do processo sequencial de junção de clusters, impõe-se que somente conglomerados (grupos de polígonos originais, como municípios, estados ou setores censitários) vizinhos possam ser unidos para formar um novo cluster maior. Neste caso, foram definidos como vizinhos polígonos que possuem um vértice em comum (vizinhança do tipo queen) ou uma aresta em comum (vizinhança do tipo rook). O estudo apresenta aplicações da nova metodologia para clusterização dos municípios brasileiros, no ano de 2000, com base em um conjunto de variáveis socioeconômicas. Diversos métodos de clusterização são estudados, assim como diferentes tipos de distâncias entre vetores. Os métodos estudados foram: centroid, single linkage, complete linkage, average linkage e average linkage weighted, Ward`s minimum variance e método da mediana. As distâncias utilizadas foram: norma Lp (em particular, as normas L1 e L2), Mahalanobis e distância euclidiana corrigida pela variância (variance corrected) - caso particular da distância de Mahalanobis. Finalmente, apresenta-se uma discussão sobre alguns métodos comumente utilizados para seleção do número de clusters. This paper presents a new methodology for hierarchical spatial clustering of contiguous polygons, based on a geographic coordinate system. The proposed algorithm is built upon a modification of traditional hierarchical clustering algorithm, commonly used in the multivariate analysis literature. According to the proposed method in this paper, at each step of the sequential process of collapsing clusters, only neighbor clusters (groups of original polygons, i.e. municipalities, census tracts, states) are allowed to be collapsed to form a bigger cluster. Two types of neighborhood are used: polygons with one edge in common (rook neighborhood) or polygons with only one point in common (queen neighborhood). In this paper, the methodology is employed to create clusters of Brazilian municipalities, for the year 2000, based on a group of socio-economic variables. Several clustering methods are investigated, as well as several types of vector distances. The studied methods were: centroid method, single linkage, complete linkage, average linkage, average linkage weighted, Ward minimum variance e median method. The studied distances were: Lp norm (particularly, L1 e L2 norms), Mahalanobis distance and variance corrected Euclidian distance. Finally, a discussion on selection of the number of clusters is presented.

Suggested Citation

  • Alexandre Xavier Ywata Carvalho & Pedro Henrique Melo Albuquerque & Gilberto Rezende de Almeida Junior & Rafael Dantas Guimarães, 2009. "Clusterização Hierárquica Espacial," Discussion Papers 1427, Instituto de Pesquisa Econômica Aplicada - IPEA.
  • Handle: RePEc:ipe:ipetds:1427
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    References listed on IDEAS

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    1. Chomitz, Kenneth M. & da Mata, Daniel & de Carvalho, Alexandre Ywata & Magalhaes, Joao Carlos, 2005. "Spatial dynamics of labor markets in Brazil," Policy Research Working Paper Series 3752, The World Bank.
    2. Juan Carlos Duque & Raúl Ramos & Jordi Suriñach, 2007. "Supervised Regionalization Methods: A Survey," International Regional Science Review, , vol. 30(3), pages 195-220, July.
    3. Kelley Pace, R. & Barry, Ronald, 1997. "Sparse spatial autoregressions," Statistics & Probability Letters, Elsevier, vol. 33(3), pages 291-297, May.
    4. L. Randall Wray & Stephanie Bell, 2004. "Introduction," Chapters,in: Credit and State Theories of Money, chapter 1 Edward Elgar Publishing.
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