  Deep convolutional neural networks (CNNs) are broadly considered to be
state-of-the-art generic end-to-end image classification systems. However, they
are known to underperform when training data are limited and thus require data
augmentation strategies that render the method computationally expensive and
not always effective. Rather than using a data augmentation strategy to encode
invariances as typically done in machine learning, here we propose to
mathematically augment a nearest subspace classification model in
sliced-Wasserstein space by exploiting certain mathematical properties of the
Radon Cumulative Distribution Transform (R-CDT), a recently introduced image
transform. We demonstrate that for a particular type of learning problem, our
mathematical solution has advantages over data augmentation with deep CNNs in
terms of classification accuracy and computational complexity, and is
particularly effective under a limited training data setting. The method is
simple, effective, computationally efficient, non-iterative, and requires no
parameters to be tuned. Python code implementing our method is available at
https://github.com/rohdelab/mathematical_augmentation. Our method is integrated
as a part of the software package PyTransKit, which is available at
https://github.com/rohdelab/PyTransKit.
