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Community detection in networks using the stochastic block model is limited in sparse graphs. However, incorporating even a small fraction of labels in a semi-supervised setting removes this limitation, enabling accurate detection across all parameters.

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Area of Science:

  • Network science
  • Statistical inference
  • Machine learning

Background:

  • The stochastic block model is a fundamental tool for network community detection.
  • A critical limitation exists at the Kesten-Stigum threshold, hindering performance on sparse graphs.
  • Existing methods struggle with performance below this threshold.

Purpose of the Study:

  • To investigate the impact of semi-supervised learning on stochastic block model limitations.
  • To demonstrate the feasibility of community detection with partial label information.
  • To develop novel algorithms for integrating network structure and labels.

Main Methods:

  • Theoretical analysis of the stochastic block model in a semi-supervised context.
  • Development of a combinatorial algorithm for label integration.
  • Development of an optimization-based algorithm for label integration.

Main Results:

  • The fundamental limitation imposed by the Kesten-Stigum threshold is overcome with partial labels.
  • Community detection becomes feasible across the entire parameter domain.
  • Two efficient algorithms are introduced, leveraging both graph topology and label data.

Conclusions:

  • Semi-supervised learning significantly enhances the capabilities of the stochastic block model.
  • The proposed algorithms offer practical solutions for community detection in real-world networks.
  • This research opens new avenues for network analysis and semidefinite programming.