Variational Auto-Encoder On Stiefel Space

Abstract

This paper presents a reformulation of Variational Auto-Encoder (VAE) framework on a non-Euclidean manifold, the Stiefel space $\stV$. By assuming the latent space to be Stiefel manifold, we can use its intrinsic orthonormality to impose structure on the learned latent space representations. We derive an objective function and gradient descendant method for learning VAE using a probabilistic distribution on the Stiefel space.