Hyperbolic Embedding of Attributed and Directed Networks

Abstract

Network embedding &#x2013; finding a low dimensional representation of the nodes with attributes in a hierarchical, directed network remains a challenging problem in the machine learning community. An emerging approach is to embed complex networks &#x2013; networks of real-world systems &#x2013; into hyperbolic space due to the fact that hyperbolic space can better naturally represent such a network&#x2019;s hierarchical structure. Existing hyperbolic embedding approaches, however, cannot handle the embedding of attributed directed networks to an arbitrary embedding dimension. To fill this gap, we introduce HEADNet, for Hyperbolic Embedding of Attributed Directed Networks, an algorithm based on extending previous works for embedding directed attributed networks to Gaussian distributions in hyperbolic space of arbitrary dimension. Through experimentation on a variety of both synthetic and real-world networks, we show that HEADNet can achieve competitive performance on common downstream machine learning tasks, including predicting directed links for previously unseen nodes. HEADNet provides an inductive hyperbolic embedding method for directed attributed networks, which opens the door to hyperbolic manifold learning on a wider range of real-world networks. The source code is freely available at <uri>https://github.com/DavidMcDonald1993/HEADNET</uri>.