  A statistical, data-driven method is presented that quantifies influences
between variables of a dynamical system. The method is based on finding a
suitable representation of points by fuzzy affiliations with respect to
landmark points using the Scalable Probabilistic Approximation algorithm. This
is followed by the construction of a linear mapping between these affiliations
for different variables and forward in time. This linear mapping can be
directly interpreted in light of unidirectional dependencies and relevant
properties of it are quantified. These quantifications then serve as measures
for the influences between variables of the dynamics. The validity of the
method is demonstrated with theoretical results and on several numerical
examples, including real-world basketball player movement.
