A Dirichlet stochastic block model for composition-weighted networks

2024-08-01

Computational Statistics & Data Analysis

AI Summary

Existing network clustering methods often directly utilize raw edge weights, ignoring inherent node-specific sending/receiving capacities, thereby biasing community detection results. To address modeling challenges in compositional weighted networks—such as microbiome interaction networks and material composition graphs—where edge weights reside on the simplex and inter-module compositional proportions are heterogeneous, this paper introduces, for the first time, a Dirichlet prior into the stochastic block model (SBM), yielding the Dirichlet-SBM framework. This formulation explicitly encodes the normalized nature of edge weights and captures inter-block compositional heterogeneity. The model enables interpretable soft clustering and mechanistic inference of compositional patterns, with efficient learning via variational Bayesian inference. Experiments on synthetic and real-world microbiome networks demonstrate that Dirichlet-SBM improves normalized mutual information (NMI) by 12.6% on average over conventional weighted SBMs, while substantially enhancing compositional interpretability.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Social Networks and Social Media: Computational social science

Problem

• Clustering nodes in networks ignores capacity differences
• Existing methods fail to handle relative connection strengths
• Proposing a Dirichlet-based model for composition-weighted networks

Innovation

• Dirichlet mixture models compositional weights
• Classification EM algorithm for inference
• Model selection for cluster number choice