An optimising approach to alternative clustering schemes

Clustering objects into groups is usually done using a statistical heuristic or an optimisation. The method depends on the size of the problem and its purpose. There may exist a number of partitions which do not differ significantly but some of which may be preferable (or equally good) when aspects of the problem not formally contained in the model are considered in the interpretation of the result. To decide between a number of good partitions they must first be enumerated and this may be done by using a number of different heuristics. In this paper an alternative method is described which uses an integer linear programming model having the number and size distribution of groups as objectives and the criteria for group membership as constraints. The model is applied to three problems each having a different measure of dissimilarity between objects and so different membership criteria. In each case a number of optimal solutions are found and expressed in two parts: a core of groups, the membership of which does not change, and the remaining objects which augment the core. The core is found to contain over three quarters of the objects and so provides a stable base for cluster definition.