Hyperbolic Node Embedding for Signed Networks

The rapid evolving World Wide Web has produced a large amount of complex and heterogeneous network data. To facilitate network analysis algorithms, signed network embedding methods automatically learn feature vectors of nodes in signed networks. However, existing algorithms only managed to embed the networks into Euclidean spaces, although many features of signed networks reported are more suitable for non-Euclidean space. Besides, previous works also do not consider the hierarchical organization of networks, which is widely existed in real-world networks. In this work, we investigate the problem of whether the hyperbolic space is a better choice to represent signed networks. We develop a non-Euclidean signed network embedding method based on structural balance theory and Riemannian optimization. Our method embeds signed networks into a Poincar\'e ball, which is a hyperbolic space can be seen as a continuous tree. This feature enables our approach to capture underlying hierarchical structure in signed networks. We empirically compare our method with three Euclidean-based baselines in visualization, sign prediction, and reconstruction tasks on six real-world datasets. The results show that our hyperbolic embedding performs better than Euclidean counterparts and can extract a meaningful latent hierarchical structure from signed networks.