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Including Node Textual Metadata in Laplacian-constrained Gaussian Graphical Models

Jianhua Wang, Killian Cressant, Pedro Braconnot Velloso, Arnaud Breloy

TL;DR

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.

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.

Including Node Textual Metadata in Laplacian-constrained Gaussian Graphical Models

TL;DR

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.

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.
Paper Structure (9 sections, 2 theorems, 29 equations, 1 figure, 1 algorithm)

This paper contains 9 sections, 2 theorems, 29 equations, 1 figure, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Problem formulation
  4. Graph learning from smooth signals
  5. Gaussian kernel graph from side information
  6. Learning from smooth signals with side-information
  7. Proposed algorithm
  8. Experimental results
  9. Conclusion

Key Result

Lemma 1

The function $f_1(\mathbf{w})$ in prob:whole:init_trans admits the following upper bound at a given point $\mathbf{w}_0$ with equality for $\mathbf{w} = \mathbf{w}_0$, where and $\mathbf{R} = \mathbf{E}^\top \mathbf{S} \mathbf{E}$ with $\tilde{\mathbf{w}}_0 \triangleq [\mathbf{w}_0^\top, 1/p]^\top$, $\tilde{\mathbf{w}} = [\mathbf{w}^\top, 1/p]^\top\in \mathbb{R}^{m+1}$ and $\mathbf{G} = [\mathbf{

Figures (1)

  • Figure 1: Evolution of the reconstructed graph as a function of $\alpha \in [0,1]$. The extreme case $\alpha = 0$ corresponds to using only side information, whereas $\alpha = 1$ corresponds to using only signal information. Intra-sector connections are represented by the corresponding sector colors, while gray-colored edges indicate connections between nodes belonging to different sectors.

Theorems & Definitions (4)

  • Lemma 1
  • proof
  • Lemma 2
  • proof