  We show how to convert any clustering into a prediction set. This has the
effect of converting the clustering into a (possibly overlapping) union of
spheres or ellipsoids. The tuning parameters can be chosen to minimize the size
of the prediction set. When applied to k-means clustering, this method solves
several problems: the method tells us how to choose k, how to merge clusters
and how to replace the Voronoi partition with more natural shapes. We show that
the same reasoning can be applied to other clustering methods.
