  Data augmentation is an area of research which has seen active development in
many machine learning fields, such as in image-based learning models,
reinforcement learning for self driving vehicles, and general noise injection
for point cloud data. However, convincing methods for general time series data
augmentation still leaves much to be desired, especially since the methods
developed for these models do not readily cross-over. Three common approaches
for time series data augmentation include: (i) Constructing a physics-based
model and then imbuing uncertainty over the coefficient space (for example),
(ii) Adding noise to the observed data set(s), and, (iii) Having access to
ample amounts of time series data sets from which a robust generative neural
network model can be trained. However, for many practical problems that work
with time series data in the industry: (i) One usually does not have access to
a robust physical model, (ii) The addition of noise can in of itself require
large or difficult assumptions (for example, what probability distribution
should be used? Or, how large should the noise variance be?), and, (iii) In
practice, it can be difficult to source a large representative time series data
base with which to train the neural network model for the underlying problem.
In this paper, we propose a methodology which attempts to simultaneously tackle
all three of these previous limitations to a large extent. The method relies
upon the well-studied matrix differential geometry of the Stiefel manifold, as
it proposes a simple way in which time series signals can placed on, and then
smoothly perturbed over the manifold. We attempt to clarify how this method
works by showcasing several potential use cases which in particular work to
take advantage of the unique properties of this underlying manifold.
