Fig. 1

Comparing empirical, high-dimensional statistical distributions. A visual example of pairwise comparison of three, standardized, bivariate normal distributions. Each point corresponds to a molecular profile measuring just two quantities. Contours are drawn to indicate regions of equal probability density. The comparison is generally based on the covariance matrix. In this case, what matters is the single covariance between the two quantities measured: positive for datasets A and B, and negative for C. Distribution of A is more similar to B than to C. In high-dimensional spaces, the contours become surfaces that form ellipsoids. Geometrically, the distributions are compared based on size and orientation of these ellipsoids. The metric of (dis)similarity proposed approximates the Symmetric Kullback–Leibler divergence and is denoted as c-SKL