  Signed network embedding methods aim to learn vector representations of nodes
in signed networks. However, existing algorithms only managed to embed networks
into low-dimensional Euclidean spaces whereas many intrinsic features of signed
networks are reported more suitable for non-Euclidean spaces. For instance,
previous works did not consider the hierarchical structures of networks, which
is widely witnessed in real-world networks. In this work, we answer an open
question that whether the hyperbolic space is a better choice to accommodate
signed networks and learn embeddings that can preserve the corresponding
special characteristics. We also propose a non-Euclidean signed network
embedding method based on structural balance theory and Riemannian
optimization, which embeds signed networks into a Poincar\'e ball in a
hyperbolic space. This space enables our approach to capture underlying
hierarchy of nodes in signed networks because it can be seen as a continuous
tree. We empirically compare our method against six Euclidean-based baselines
in three tasks on seven real-world datasets, and the results show the
effectiveness of our method.
