Clustering with a constraining variable

Clustering can be treated as an optimization problem over a set of feasible clusterings. This paper deals with a clustering problem where the set of feasible clusterings is determined by constraining the function of values of a given (constraining) variable in each cluster. It can be shown that agglomerative clustering methods are not suitable for solving problems with constraining variables. For solving clustering problems of this type, local optimization procedures can be adapted. In the study of the influence of constraints on the clustering, a special coefficient is defined. The proposed procedures of clustering with constraining variables are illustrated by clustering the Slovene communes on the basis of the socioeconomic indicators.