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Broad spectrum structure discovery in large-scale higher-order networks.

John Hood1, Caterina De Bacco2, Aaron Schein3

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This study introduces a new probabilistic model for analyzing complex systems represented as hypergraphs. The model efficiently discovers mesoscale structures, improving predictions and understanding of higher-order interactions.

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Area of Science:

  • Network Science
  • Computational Biology
  • Sociology

Background:

  • Complex systems exhibit higher-order interactions, often modeled as hypergraphs.
  • Understanding hypergraph structures is vital but computationally challenging due to combinatorial complexity.

Purpose of the Study:

  • To develop a probabilistic model for efficient representation and discovery of mesoscale structures in large-scale hypergraphs.
  • To enable tractable capture of rich structural patterns and ensure model identifiability.

Main Methods:

  • Introduced a novel class of probabilistic models.
  • Treated classes of similar units as nodes in a latent hypergraph.
  • Modeled observed interactions via latent class interactions using low-rank representations.

Main Results:

  • The model efficiently represents and discovers mesoscale structures in hypergraphs.
  • Achieved improved link prediction performance compared to state-of-the-art methods.
  • Discovered interpretable node- and class-level structures in real-world networks.

Conclusions:

  • The proposed model offers a tractable approach to analyzing large-scale hypergraphs.
  • Enhances the ability to incorporate higher-order interaction data into scientific analysis.
  • Demonstrates utility in diverse fields like pharmacology and social network analysis.