  Many approaches in the field of machine learning and data analysis rely on
the assumption that the observed data lies on lower-dimensional manifolds. This
assumption has been verified empirically for many real data sets. To make use
of this manifold assumption one generally requires the manifold to be locally
sampled to a certain density such that features of the manifold can be
observed. However, for increasing intrinsic dimensionality of a data set the
required data density introduces the need for very large data sets, resulting
in one of the many faces of the curse of dimensionality. To combat the
increased requirement for local data density we propose a framework to generate
virtual data points that faithful to an approximate embedding function
underlying the manifold observable in the data.
