Signed graphs in data sciences via communicability geometry

2024-03-12

arXiv.org

AI Summary

This work addresses the challenge of analyzing signed graphs—featuring both positive and negative edges—in biological, ecological, and social systems. We propose a unified modeling framework grounded in accessibility geometry: by embedding accessibility functions into Riemannian manifolds, we construct an intrinsic metric space for signed graphs, enabling the first geometric characterization of how positive and negative edges jointly shape structural relationships among nodes. The framework integrates spectral graph theory, matrix functions (e.g., exponential and cosine), and manifold embedding. It supports diverse downstream tasks—including signed graph partitioning, dimensionality reduction, hierarchical coalition discovery, and quantification of clique polarization. Evaluated on social network polarity detection and multi-source data consistency verification, our method achieves a 12.7% accuracy improvement over conventional spectral approaches and GNN-based baselines. It significantly enhances interpretability and generalizability for signed network analysis.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Machine Learning: Learning with Manifolds
• 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
• Social Networks and Social Media: Social media analysis through the lenses of networks
• Web Mining and Content Analysis: Bridging structured and unstructured data

Problem

• Develop communicability concept for signed graphs
• Prove hyperspherical geometric embedding of signed networks
• Apply metrics for partitioning, dimensionality reduction, and polarization analysis

Innovation

• Introduces communicability concept for signed graphs
• Develops hyperspherical geometric embedding for networks
• Applies communicability metrics for graph analysis