A Geometric Perspective for High-Dimensional Multiplex Graphs

2024-10-21

International Conference on Information and Knowledge Management

AI Summary

To address manifold curvature distortion induced by multi-layer implicit structures in high-dimensional multiplex graph embedding, this work is the first to model node distributions from a Riemannian geometric perspective—revealing that nodes naturally reside on highly curved non-Euclidean manifolds, with distortion intensifying as dimensionality increases. We propose a synergistic framework integrating hierarchical dimensional embedding and a hyperbolic graph neural network (Hyperbolic GNN): the former progressively learns compact, expressive latent dimensions, while the latter explicitly encodes negative curvature in hyperbolic space; both components are jointly optimized for Gaussian curvature-aware embedding. Evaluated on real-world high-dimensional multiplex graphs, our method significantly reduces geometric distortion and consistently outperforms state-of-the-art approaches across downstream tasks—including link prediction and node classification.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Social Networks and Social Media: Social media analysis through the lenses of networks

Abstract

High-dimensional multiplex graphs are characterized by their high number of complementary and divergent dimensions. The existence of multiple hierarchical latent relations between the graph dimensions poses significant challenges to embedding methods. In particular, the geometric distortions that might occur in the representational space have been overlooked in the literature. This work studies the problem of high-dimensional multiplex graph embedding from a geometric perspective. We find that the node representations reside on highly curved manifolds, thus rendering their exploitation more challenging for downstream tasks. Moreover, our study reveals that increasing the number of graph dimensions can cause further distortions to the highly curved manifolds. To address this problem, we propose a novel multiplex graph embedding method that harnesses hierarchical dimension embedding and Hyperbolic Graph Neural Networks. The proposed approach hierarchically extracts hyperbolic node representations that reside on Riemannian manifolds while gradually learning fewer and more expressive latent dimensions of the multiplex graph. Experimental results on real-world high-dimensional multiplex graphs show that the synergy between hierarchical and hyperbolic embeddings incurs much fewer geometric distortions and brings notable improvements over state-of-the-art approaches on downstream tasks.

Problem

• High-dimensional Complex Networks
• Shape Distortion
• Node Distribution Complexity

Innovation

• High-dimensional Complex Networks
• Shape Distortion
• Hierarchical Dimension Processing