Model-based clustering for random hypergraphs

Area of Science:

• Computational statistics
• Network science
• Data mining

Background:

• Real-world data often involves complex, higher-order interactions beyond simple pairwise relationships.
• Existing models may not adequately capture the variability in interaction structures or the varying number of objects involved in an interaction (hyperedge size).

Purpose of the Study:

• To introduce a novel probabilistic model for random hypergraphs capable of representing diverse interaction orders.
• To extend latent class analysis (LCA) by incorporating specific structures for hyperedges to account for size variations.
• To develop robust methods for parameter estimation and model selection.

Main Methods:

• Development of a probabilistic hypergraph model as an extension of latent class analysis.
• Implementation of an expectation-maximization algorithm incorporating minorization-maximization steps for parameter estimation.
• Application of the Bayesian Information Criterion (BIC) for model selection.

Main Results:

• The proposed model effectively represents unary, binary, and higher-order interactions.
• The model captures variations in hyperedge sizes through its dual clustering structures.
• Successful application to simulated data and two real-world datasets yielded significant findings.

Conclusions:

• The introduced probabilistic hypergraph model provides a flexible framework for analyzing complex systems with higher-order interactions.
• The developed estimation and selection procedures are effective for practical application.
• The model demonstrates potential for uncovering meaningful patterns in diverse real-world datasets.