Fuzzy clustering with structural constraints

In this paper we propose a generalization of the standard clustering problem, which we call Structural Constrained Clustering (SCC) problem. In SCC problem, the cluster interconnections are given by a binary relation R. If this relation is empty then SCC problem reduces to the standard classification problem. The duster structure imposed by R may be described by the covering graph of R, For example, if this graph is a rooted tree then a hierarchical structure is imposed to the clusters. We formulate SCC as a fuzzy clustering problem with prototype inter-relation A general algorithm to solve this problem is proposed. For three particular distance measures (squared, Euclidean and L-1 metric) we compute the prototypes by solving a particular multifacility location problem. (C) 1999 Elsevier Science B.V. All rights reserved.