The convergence of some clustering techniques for elements ideally grouped in clusters

Depending on the characteristics of the clusters we want to determine, different clus- tering techniques are employed. Data characterization is usually not perfect, the model suffers and the clustering results are not always what the user expected. This paper argues that, for elements ideally grouped in clusters, clustering techniques converges. We propose a characterization of elements ide- ally grouped in clusters and prove the uniqueness of the optimumclusters for some different clustering criteria.