Chapter 11 Spatially Constrained Clustering - Partitioning Methods

This third chapter devoted to spatial clustering focuses on the inclusion of explicit spatial constraints in partitioning methods. As mentioned in the previous chapter, in the literature, this is often referred to as the p-regions problem.

A discussion of the general issues and extensive literature reviews can be found in Duque, Ramos, and Suriñach (2007), Duque, Church, and Middleton (2011), and Li, Church, and Goodchild (2014), among others. Here, the focus of attention is on two specific approaches: AZP and max-p. 

In the automatic zoning problem or AZP, originally considered by Openshaw (1977) (later, AZP is also referred to as the automatic zoning procedure), a prior specification of the number of zones or regions (\(p\)) is required. In previous chapters, the number of regions was referred to as \(k\), but for consistency with the max-p and p-region terminology, \(p\) is used here.

In contrast, in the so-called max-p regions model, proposed in Duque, Anselin, and Rey (2012), the number of regions becomes endogenous, and heuristics are developed to find the allocation of spatial units into the largest number of regions (max-p), such that a spatially extensive minimum threshold condition is met.

These techniques are again illustrated with the Ceará Zika sample data set, using the same six variables and queen contiguity weights as before.