  We discuss the inadequacy of covariances/correlations and other measures in
L2 as relative distance metrics under some conditions. We propose a
computationally simple heuristic to transform a map based on standard principal
component analysis (PCA) (when the variables are asymptotically Gaussian) into
an entropy-based map where distances are based on mutual information (MI).
Rescaling Principal Component based distances using MI allows a representation
of relative statistical associations when, as in genetics, it is applied on bit
measurements between individuals' genomic mutual information.
  This entropy rescaled PCA, while preserving order relationships (along a
dimension), changes the relative distances to make them linear to information.
We show the effect on the entire world population and some subsamples, which
leads to significant differences with the results of current research.
