Does dimensionality reduction improve the quality of motion interpolation?

In recent years nonlinear dimensionality reduction has frequently been suggested for the modelling of high-dimensional motion data. While it is intuitively plausible to use dimensionality reduction to recover low dimensional manifolds which compactly represent a given set of movements, there is a lack of critical investigation into the quality of resulting representations, in particular with respect to generalisability. Furthermore it is unclear how consistently particular methods can achieve good results. Here we use a set of robotic motion data for which we know the ground truth to evaluate a range of nonlinear dimensionality reduction methods with respect to the quality of motion interpolation. We show that results are extremely sensitive to parameter settings and data set used, but that dimensionality reduction can potentially improve the quality of linear motion interpolation, in particular in the presence of noise.