  Most of the existing literature regarding hyperbolic embedding concentrate
upon supervised learning, whereas the use of unsupervised hyperbolic embedding
is less well explored. In this paper, we analyze how unsupervised tasks can
benefit from learned representations in hyperbolic space. To explore how well
the hierarchical structure of unlabeled data can be represented in hyperbolic
spaces, we design a novel hyperbolic message passing auto-encoder whose overall
auto-encoding is performed in hyperbolic space. The proposed model conducts
auto-encoding the networks via fully utilizing hyperbolic geometry in message
passing. Through extensive quantitative and qualitative analyses, we validate
the properties and benefits of the unsupervised hyperbolic representations.
Codes are available at https://github.com/junhocho/HGCAE.
