  The statistical analysis of data lying on a differentiable, locally
Euclidean, manifold introduces a variety of challenges because the analogous
measures to standard Euclidean statistics are local, that is only defined
within a neighbourhood of each datapoint. This is because the curvature of the
space means that the connection of Riemannian geometry is path dependent. In
this paper we transfer the problem to Weitzenb\"{o}ck space, which has torsion,
but not curvature, meaning that parallel transport is path independent, and
rather than considering geodesics, it is natural to consider autoparallels,
which are `straight' in the sense that they follow the local basis vectors. We
demonstrate how to generate these autoparallels in a data-driven fashion, and
show that the resulting representation of the data is a useful space in which
to perform further analysis.
