[2Q5-J-2] Machine learning: advanced models

[2Q5-J-2-04] Variational Auto-Encoder On Stiefel Space

〇Takaaki Sanjoh¹, Junpei Komiyama², Masashi Toyoda², Masaru Kitsuregawa^2,3 (1. The University of Tokyo, 2. Institute of Industrial Science, The University of Tokyo, 3. National Institute of Informatics)

Keywords:Variational Auto-Encoder, Manifold Learning, Stiefel space

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.