Community detection in hypergraphs via mutual information maximization.

Area of Science:

• Computer Science
• Data Mining
• Network Analysis

Background:

• Hypergraph community detection aims to find related vertex groups within complex hypergraph data structures.
• Existing algorithms often rely on canonical models requiring inference of statistical parameters, limiting their applicability.

Purpose of the Study:

• To propose a novel information-theoretic algorithm for hypergraph community detection.
• To develop a method that compresses hypergraph data using community labels and edge intersections.
• To offer an alternative to parameter-inference-dependent algorithms by using a microcanonical stochastic blockmodel.

Main Methods:

• An information-theoretic approach is employed for hypergraph community detection.
• Data compression is achieved through community labels and community-edge intersections.
• Maximum-likelihood inference is performed using simulated annealing within a degree-corrected microcanonical stochastic blockmodel.

Main Results:

• The proposed microcanonical algorithm successfully identifies communities in sparse random hypergraphs, even at conjectured thresholds.
• It demonstrates competitive performance in cluster recovery tasks across various hypergraph datasets.
• The algorithm avoids the need to infer statistical parameters like vertex degrees or group connection rates.

Conclusions:

• The developed information-theoretic algorithm offers an effective and efficient solution for hypergraph community detection.
• Its microcanonical approach provides advantages over canonical models by simplifying the inference process.
• The method shows strong performance and robustness on both synthetic and real-world hypergraph data.