Optimization in non-hierarchical clustering

Algorithms which are operationally efficient and which give a good partition of a finite set, produce solutions that are not necessarily optimum. The main aim of this paper is a synthetical study of properties of optimality in spaces formed by partitions of a finite set. We formalize and take for a model of that study a family of particularly efficient technics of “clusters centers” type. The proposed algorithm operates on groups of points or “kernels” these kernels adapt and evolve into interesting clusters. After having developed the notion of “strong” and “weak” patterns, and the computer aspects, we illustrate the different results by an artificial example and by two applications: one in mineral geology, the other in medicine to determine biological profiles.