An Adjacency Constraint in Agglomerative Hierarchical Classifications of Geographic Data

Abstract

A numerical method for classifying geographic data is presented which incorporates geographic location as an external constraint. The method was implemented by making minimal changes to an existing agglomerative hierarchical algorithm. This was seen as the simplest solution, both computationally and operationally. Given a matrix of similarities or distances calculated from the usual intrinsic variables, the classification proceeds normally with the constraint that only adjacent objects are allowed to form groups. The method has been implemented previously, but here the examination of it is extended to cover the effects of a range of different fusion strategies, and to consider changes in within-group heterogeneity as a result of imposing an adjacency constraint. Three other matters arising are discussed: the presence of regional as opposed to global outliers of a classification; the occurrence of reversals in similarity values; and a measure of the stress imposed on a classification with an adjacency constraint. The method is seen as suggesting a possible general solution to the problem of constraints in numerical classification. Some examples of other constraints and the appropriate fusion strategies are given.