  Deep learning has yielded remarkable outcomes in various domains. However,
the challenge of requiring large-scale labeled samples still persists in deep
learning. Thus, data augmentation has been introduced as a critical strategy to
train deep learning models. However, data augmentation suffers from information
loss and poor performance in small sample environments. To overcome these
drawbacks, we propose a feature augmentation method based on shape space
theory, i.e., feature augmentation on Geodesic curve, called FAGC in
brevity.First, we extract features from the image with the neural network
model. Then, the multiple image features are projected into a pre-shape space
as features. In the pre-shape space, a Geodesic curve is built to fit the
features. Finally, the many generated features on the Geodesic curve are used
to train the various machine learning models. The FAGC module can be seamlessly
integrated with most machine learning methods. And the proposed method is
simple, effective and insensitive for the small sample datasets.Several
examples demonstrate that the FAGC method can greatly improve the performance
of the data preprocessing model in a small sample environment.
