  The increasing application of deep-learning is accompanied by a shift towards
highly non-linear statistical models. In terms of their geometry it is natural
to identify these models with Riemannian manifolds. The further analysis of the
statistical models therefore raises the issue of a correlation measure, that in
the cutting planes of the tangent spaces equals the respective Pearson
correlation and extends to a correlation measure that is normalized with
respect to the underlying manifold. In this purpose the article reconstitutes
elementary properties of the Pearson correlation to successively derive a
linear generalization to multiple dimensions and thereupon a nonlinear
generalization to principal manifolds, given by the Riemann-Pearson
Correlation.
