  In order to analyze and extract different structural properties of
distributions, one can introduce different coordinate systems over the manifold
of distributions. In Evolutionary Computation, the Walsh bases and the Building
Block Bases are often used to describe populations, which simplifies the
analysis of evolutionary operators applying on populations. Quite independent
from these approaches, information geometry has been developed as a geometric
way to analyze different order dependencies between random variables (e.g.,
neural activations or genes).
  In these notes I briefly review the essentials of various coordinate bases
and of information geometry. The goal is to give an overview and make the
approaches comparable. Besides introducing meaningful coordinate bases,
information geometry also offers an explicit way to distinguish different order
interactions and it offers a geometric view on the manifold and thereby also on
operators that apply on the manifold. For instance, uniform crossover can be
interpreted as an orthogonal projection of a population along an m-geodesic,
monotonously reducing the theta-coordinates that describe interactions between
genes.
