  Finding a low dimensional representation of hierarchical, structured data
described by a network remains a challenging problem in the machine learning
community. An emerging approach is embedding these networks into hyperbolic
space because it can naturally represent a network's hierarchical structure.
However, existing hyperbolic embedding approaches cannot deal with attributed
networks, in which nodes are annotated with additional attributes. These
attributes might provide additional proximity information to constrain the
representations of the nodes, which is important to learn high quality
hyperbolic embeddings. To fill this gap, we introduce HEAT (Hyperbolic
Embedding of ATributed networks), the first method for embedding attributed
networks to a hyperbolic space. HEAT consists of 1) a modified random walk
algorithm to obtain training samples that capture both topological and
attribute similarity; and 2) a learning algorithm for learning hyperboloid
embeddings from the obtained training samples. We show that by leveraging node
attributes, HEAT can outperform a state-of-the-art Hyperbolic embedding
algorithm on several downstream tasks. As a general embedding method, HEAT
opens the door to hyperbolic manifold learning on a wide range of attributed
and unattributed networks.
