Clusterização hierárquica espacial com atributos binários

This paper studies a methodology for hierarchical spatial clustering of contiguous and homogeneous polygons, based on a set of binary variables. The proposed algorithm is built upon a modification of traditional agglomerative 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, based on the increase or decrease in the number of jobs between 1997 and 2007. Several clustering methods are investigated, as well as several types of vector distances for binary variables. 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: Jaccard, Tanimoto, simple matching, Russel e Rao, Dice, Kulczynski. A discussion on selection of the number of clusters is presented. Finally, case studies are presented in order to: (a) compare the intra-cluster variability of spatial hierarchical clusters versus the intra-cluster variability of existing political agglomerations (states, micro-regions and meso-regions); (b) identify areas or diversified economic growth.