Mapping bipartite networks into multidimensional hyperbolic spaces

2025-03-06

AI Summary

To address spurious associations and cluster inflation caused by unimodal projections in bipartite network modeling, this paper proposes a projection-free paradigm that jointly embeds both node types directly into a multidimensional hyperbolic space. Methodologically, it introduces bipartite 4-cycle density as a geometric clustering metric—ensuring structural fidelity—and designs the B-Mercator algorithm, which performs end-to-end hyperbolic coordinate inference via maximum likelihood estimation. Crucially, the approach eliminates manually imposed distance distortions, allowing connection probabilities to naturally follow the hyperbolic distance decay law. Experiments on diverse real-world datasets demonstrate significant improvements in node classification and distance-based link prediction. Moreover, the framework enables high-fidelity, privacy-preserving synthetic network generation. Key contributions include: (i) the first use of bipartite 4-cycle density for hyperbolic clustering; (ii) a principled, projection-free embedding method grounded in statistical inference; and (iii) empirically validated gains in predictive accuracy and generative capability.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for 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

Bipartite networks appear in many real-world contexts, linking entities across two distinct sets. They are often analyzed via one-mode projections, but such projections can introduce artificial correlations and inflated clustering, obscuring the true underlying structure. In this paper, we propose a geometric model for bipartite networks that leverages the high levels of bipartite four-cycles as a measure of clustering to place both node types in the same similarity space, where link probabilities decrease with distance. Additionally, we introduce B-Mercator, an algorithm that infers node positions from the bipartite structure. We evaluate its performance on diverse datasets, illustrating how the resulting embeddings improve downstream tasks such as node classification and distance-based link prediction in machine learning. These hyperbolic embeddings also enable the generation of synthetic networks with node features closely resembling real-world ones, thereby safeguarding sensitive information while allowing secure data sharing. In addition, we show how preserving bipartite structure avoids the pitfalls of projection-based techniques, yielding more accurate descriptions and better performance. Our method provides a robust framework for uncovering hidden geometry in complex bipartite systems.

Problem

• Mapping bipartite networks into hyperbolic spaces to reveal true structure.
• Avoiding artificial correlations from one-mode projections in network analysis.
• Improving node classification and link prediction with hyperbolic embeddings.

Innovation

• Geometric model for bipartite networks using hyperbolic spaces
• B-Mercator algorithm infers node positions from structure
• Hyperbolic embeddings improve node classification and link prediction