Including Node Textual Metadata in Laplacian-constrained Gaussian Graphical Models

2026-02-17

AI Summary

This work addresses the limitation of traditional Gaussian graphical models, which neglect node-associated textual metadata during graph structure learning, leading to suboptimal use of available information. To overcome this, the authors propose a Laplacian-constrained Gaussian graphical model that jointly integrates node signals and textual metadata—marking the first incorporation of text information into this modeling framework. The resulting approach enables unified modeling of multi-source heterogeneous data. An efficient majorization-minimization (MM) optimization algorithm is employed, yielding a closed-form solution at each iteration and ensuring rapid convergence. Experimental results on real-world financial datasets demonstrate that the proposed method significantly outperforms existing approaches that rely solely on either signals or metadata, achieving substantial improvements in graph clustering performance.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text

Abstract

This paper addresses graph learning in Gaussian Graphical Models (GGMs). In this context, data matrices often come with auxiliary metadata (e.g., textual descriptions associated with each node) that is usually ignored in traditional graph estimation processes. To fill this gap, we propose a graph learning approach based on Laplacian-constrained GGMs that jointly leverages the node signals and such metadata. The resulting formulation yields an optimization problem, for which we develop an efficient majorization-minimization (MM) algorithm with closed-form updates at each iteration. Experimental results on a real-world financial dataset demonstrate that the proposed method significantly improves graph clustering performance compared to state-of-the-art approaches that use either signals or metadata alone, thus illustrating the interest of fusing both sources of information.

Problem

• Gaussian Graphical Models
• graph learning
• textual metadata
• node metadata
• Laplacian-constrained

Innovation

• Laplacian-constrained GGMs
• graph learning
• textual metadata
• majorization-minimization algorithm
• graph clustering