Two derivations of Principal Component Analysis on datasets of
  distributions
Vlad Niculae
In this brief note, we formulate Principal Component Analysis (PCA) over
datasets consisting not of points but of distributions, characterized by their
location and covariance. Just like the usual PCA on points can be equivalently
derived via a variance-maximization principle and via a minimization of
reconstruction error, we derive a closed-form solution for distributional PCA
from both of these perspectives.