Carvalho, Alexandre Xavier Ywata Albuquerque, Pedro Henrique Melo de Almeida Junior, Gilberto Rezende Guimarães, Rafael Dantas
Year of Publication:
Texto para Discussão, Instituto de Pesquisa Econômica Aplicada (IPEA) 1427
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.