Thinning out redundant empirical data

Given a set X of ``empirical" points, whose coordinates are perturbed by errors, we analyze whether it contains redundant information, that is whether some of its elements could be represented by a single equivalent point. If this is the case, the empirical information associated to X could be described by fewer points, chosen in a suitable way. We present two different methods to reduce the cardinality of X which compute a new set of points equivalent to the original one, that is representing the same empirical information. Though our algorithms use basic notions of Cluster Analysis they are specifically designed for ``thinning out" redundant data. We include some experimental results which illustrate the practical effectiveness of our methods