T-GINEE: A Tensor-Based Multi-Graph Representation Learning

While traditional network analysis focuses on single-layer networks, real-world systems often form multilayer networks with multiple relationship types. However, existing methods typically fail to capture complex inter-layer dependencies by treating layers independently or aggregating them. To address this, we propose T-GINEE (Tensor-Based Generalized Multilayer-graph Estimating Equation), a statistical regularization framework combining tensor-based generalized estimating equations with task-specific loss to model cross-network correlations explicitly. Key innovations include: (1) CP tensor decomposition capturing structural dependencies via shared latent factors; (2) a generalized estimating equation framework modeling inter-layer correlations through working covariance matrices; and (3) a flexible link function accommodating characteristics like sparsity. Our theoretical analysis establishes consistency and asymptotic normality under mild conditions. Extensive experiments on synthetic and real-world datasets validate T-GINEE’s effectiveness for multilayer network analysis. Our code is available in the \textbf{supplementary materials} to ensure reproducibility.

People interact through multiple types of relationships simultaneously, such as friendships, professional ties, or collaborations, and these connections influence each other. Yet most methods analyze each relationship type separately, missing important cross-network patterns. We developed T-GINEE, a framework that analyzes multiple overlapping networks together by explicitly modeling how different relationship types correlate. It finds shared characteristics for each person that explain their connectivity across all relationship types at once. We proved our method produces reliable estimates under mild conditions and showed it outperforms existing approaches at predicting missing connections, scaling to networks with millions of users.