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.

翻译：本文研究高斯图模型中的图学习问题。在此背景下，数据矩阵常伴随辅助元数据（例如与每个节点关联的文本描述），而传统图估计方法通常忽略此类信息。为填补这一空白，我们提出一种基于拉普拉斯约束高斯图模型的图学习方法，该方法能同时利用节点信号与元数据。所得公式导出一个优化问题，我们为此设计了一种高效的主最小化算法，该算法在每次迭代中均具有闭式更新。在真实金融数据集上的实验结果表明，相较于仅使用信号或元数据的现有先进方法，所提方案能显著提升图聚类性能，从而验证了融合两类信息源的价值。