The Variational Auto-Encoder (VAE) is one of the most used unsupervised machine learning models. But although the default choice of a Gaussian distribution for both the prior and posterior represents a mathematically convenient distribution often leading to competitive results, we show that this parameterization fails to model data with a latent hyperspherical structure. To address this issue we propose using a von Mises-Fisher (vMF) distribution instead, leading to a hyperspherical latent space. Through a series of experiments we show how such a hyperspherical VAE, or S-VAE, is more suitable for capturing data with a hyperspherical latent structure, while outperforming a normal, N -VAE, in low dimensions on other data types.
The approach most similar to ours but with a hyperspherical latent space and a von-Mises variational distribution has been presented in REF .
Hyperspherical Variational Auto-Encoders
Uncertainty in Artificial Intelligence (UAI). Proceedings of the Thirty-Fourth Conference (2018) 856- 865
Computer Science Mathematics