Hyperbolic embedding of attributed and directed networks

David McDonald, Shan He

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Network embedding – 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 – networks of real-world systems – into hyperbolic space due to the fact that hyperbolic space can better naturally represent such a network’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 https://github.com/DavidMcDonald1993/HEADNET.
Original languageEnglish
Article number9815143
Pages (from-to)7003-7015
Number of pages13
JournalIEEE Transactions on Knowledge and Data Engineering
Issue number7
Early online date4 Jul 2022
Publication statusPublished - Jul 2023

Bibliographical note

Publisher Copyright:


  • Attributed network embedding
  • complex networks
  • directed network embedding
  • hyperbolic embedding
  • Uncertainty
  • Computational modeling
  • Neural networks
  • Complex networks
  • Gaussian distribution
  • Extraterrestrial measurements
  • Task analysis

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Computational Theory and Mathematics


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