TimewarpVAE: Simultaneous Time-Warping and Representation Learning of
  Trajectories
Travers Rhodes Daniel D. Lee
Human demonstrations of trajectories are an important source of training data
for many machine learning problems. However, the difficulty of collecting human
demonstration data for complex tasks makes learning efficient representations
of those trajectories challenging. For many problems, such as for handwriting
or for quasistatic dexterous manipulation, the exact timings of the
trajectories should be factored from their spatial path characteristics. In
this work, we propose TimewarpVAE, a fully differentiable manifold-learning
algorithm that incorporates Dynamic Time Warping (DTW) to simultaneously learn
both timing variations and latent factors of spatial variation. We show how the
TimewarpVAE algorithm learns appropriate time alignments and meaningful
representations of spatial variations in small handwriting and fork
manipulation datasets. Our results have lower spatial reconstruction test error
than baseline approaches and the learned low-dimensional representations can be
used to efficiently generate semantically meaningful novel trajectories.