# Hyperspherical Variational Auto-Encoders

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 $\mathcal{S}$-VAE, is more suitable for capturing data with a hyperspherical latent structure, while outperforming a normal, $\mathcal{N}$-VAE, in low dimensions on other data types.

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## Results from the Paper Edit

Task Dataset Model Metric Name Metric Value Global Rank Result Benchmark
Link Prediction Citeseer S-VGAE AUC 94.7 # 6
AP 95.2 # 6
Link Prediction Cora VGNAE AUC 94.1% # 4
AP 94.1% # 4
Link Prediction Pubmed S-VGAE AUC 96.0% # 5
AP 96.0% # 6