Data Augmentation in High Dimensional Low Sample Size Setting Using a Geometry-Based Variational Autoencoder.

In this paper, we propose a new method to perform data augmentation in a reliable way in the High Dimensional Low Sample Size (HDLSS) setting using a geometry-based variational autoencoder (VAE). Our approach combines the proposal of 1) a new VAE model, the latent space of which is modeled as a Riemannian manifold and which combines both Riemannian metric learning and normalizing flows and 2) a new generation scheme which produces more meaningful samples especially in the context of small data sets. The method is tested through a wide experimental study where its robustness to data sets, classifiers and training samples size is stressed.