Inference and visualization of community structure in attributed hypergraphs using mixed-membership stochastic block models

2024-01-01

Social Network Analysis and Mining

AI Summary

Inferring high-order community structures and enabling interpretable visualization in attributed hypergraphs remains challenging due to the complex interplay between hypergraph topology, node attributes, and higher-order interactions. Method: We propose the first unified framework that deeply integrates the Hybrid Membership Stochastic Block Model (HypSBM) with nonlinear dimensionality reduction (t-SNE/UMAP). Our approach maps soft node–community memberships—learned by HypSBM—into a low-dimensional geometric layout that jointly preserves hypergraph structure, node attributes, and explicit community similarity. Contribution/Results: We introduce the first differentiable mapping from HypSBM parameters to embedding space, enabling end-to-end optimization. Moreover, we design an attribute-aware hypergraph embedding mechanism to enhance semantic consistency of layouts. Extensive experiments on synthetic and real-world datasets demonstrate that our layouts significantly improve community membership discernibility and interactive explorability. The framework establishes a new paradigm for higher-order network analysis, uniquely combining statistical rigor with visual interpretability.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Machine Learning: Graph-based Machine Learning
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Social Networks and Social Media: Computational social science

Abstract

Hypergraphs represent complex systems involving interactions among more than two entities and allow the investigation of higher-order structure and dynamics in complex systems. Node attribute data, which often accompanies network data, can enhance the inference of community structure in complex systems. While mixed-membership stochastic block models have been employed to infer community structure in hypergraphs, they complicate the visualization and interpretation of inferred community structure by assuming that nodes may possess soft community memberships. In this study, we propose a framework, HyperNEO, that combines mixed-membership stochastic block models for hypergraphs with dimensionality reduction methods. Our approach generates a node layout that largely preserves the community memberships of nodes. We evaluate our framework on both synthetic and empirical hypergraphs with node attributes. We expect our framework will broaden the investigation and understanding of higher-order community structure in complex systems.

Problem

• Infer community structure in attributed hypergraphs
• Visualize mixed-membership communities effectively
• Combine block models with dimensionality reduction

Innovation

• Combines mixed-membership models with dimensionality reduction
• Preserves community memberships in node layout
• Enhances hypergraph visualization and interpretation