  In this paper we introduce three methods for re-scaling data sets aiming at
improving the likelihood of clustering validity indexes to return the true
number of spherical Gaussian clusters with additional noise features. Our
method obtains feature re-scaling factors taking into account the structure of
a given data set and the intuitive idea that different features may have
different degrees of relevance at different clusters.
  We experiment with the Silhouette (using squared Euclidean, Manhattan, and
the p$^{th}$ power of the Minkowski distance), Dunn's, Calinski-Harabasz and
Hartigan indexes on data sets with spherical Gaussian clusters with and without
noise features. We conclude that our methods indeed increase the chances of
estimating the true number of clusters in a data set.
