Informational Rescaling of PCA Maps with Application to Genetic Distance

March, 2023

Abstract

We discuss the inadequacy of covariances/correlations and other measures in L-2 as relative distance metrics. 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 PCA distances using MI allows a representation of relative correlations. This entropy rescaled PCA, while preserving order relationships, changes the relative distances to make them linear to information.