# Leveraging Low-rank Factorizations of Conditional Correlation Matrices in Graph Learning

arXiv: https://arxiv.org/abs/2506.10628 · HTML: https://mlsanity.com/paper/2506.10628/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 96 references that are in the map.
- First posted on arXiv 12 Jun 2025.

## Builds on (most cited first, 30 of 31)

- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [How to learn a graph from smooth signals](https://mlsanity.com/paper/1601.02513/) (2016)
- [Connecting the Dots: Identifying Network Structure via Graph Signal Processing](https://mlsanity.com/paper/1810.13066/) (2018)
- [Graph signal processing for machine learning: A review and new perspectives](https://mlsanity.com/paper/2007.16061/) (2020)
- [Riemannian SVRG: Fast Stochastic Optimization on Riemannian Manifolds](https://mlsanity.com/paper/1605.07147/) (2016)
- [A Unified Framework for Structured Graph Learning via Spectral Constraints](https://mlsanity.com/paper/1904.09792/) (2019)
- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Graph Signal Processing: History, Development, Impact, and Outlook](https://mlsanity.com/paper/2303.12211/) (2023)
- [Large Scale Graph Learning from Smooth Signals](https://mlsanity.com/paper/1710.05654/) (2017)
- [Fluid Communities: A Competitive, Scalable and Diverse Community Detection Algorithm](https://mlsanity.com/paper/1703.09307/) (2017)
- [Network Enhancement: a general method to denoise weighted biological networks](https://mlsanity.com/paper/1805.03327/) (2018)
- [Maximum likelihood estimation in Gaussian models under total positivity](https://mlsanity.com/paper/1702.04031/) (2017)
- [MADMM: a generic algorithm for non-smooth optimization on manifolds](https://mlsanity.com/paper/1505.07676/) (2015)
- [Estimation of Graphical Models through Structured Norm Minimization](https://mlsanity.com/paper/1609.09010/) (2016)
- [A Proximal Approach for a Class of Matrix Optimization Problems](https://mlsanity.com/paper/1801.07452/) (2018)
- [Fast Projected Newton-like Method for Precision Matrix Estimation under Total Positivity](https://mlsanity.com/paper/2112.01939/) (2021)
- [Learning Graphical Factor Models with Riemannian Optimization](https://mlsanity.com/paper/2210.11950/) (2022)
- [Polynomial Graphical Lasso: Learning Edges from Gaussian Graph-Stationary Signals](https://mlsanity.com/paper/2404.02621/) (2024)
- [Verifying the Smoothness of Graph Signals: A Graph Signal Processing Approach](https://mlsanity.com/paper/2305.19618/) (2023)
- [Learning Large-Scale MTP2 Gaussian Graphical Models via Bridge-Block Decomposition](https://mlsanity.com/paper/2309.13405/) (2023)
- [The Fisher-Rao geometry of CES distributions](https://mlsanity.com/paper/2310.01032/) (2023)
- [On the inconsistency of ℓ1-penalised sparse precision matrix estimation](https://mlsanity.com/paper/1603.02532/) (2016)
- [Efficient Graph Laplacian Estimation by Proximal Newton](https://mlsanity.com/paper/2302.06434/) (2023)
- [Elliptical graphical modelling](https://mlsanity.com/paper/1506.04321/) (2015)
- [Computation of the Maximum Likelihood estimator in low-rank Factor Analysis](https://mlsanity.com/paper/1801.05935/) (2018)
- [Riemannian geometry for Compound Gaussian distributions: application to recursive change detection](https://mlsanity.com/paper/2005.10087/) (2020)
- [Bayesian Scalable Precision Factor Analysis for Massive Sparse Gaussian Graphical Models](https://mlsanity.com/paper/2107.11316/) (2021)
- [Low-rank covariance matrix estimation for factor analysis in anisotropic noise: application to array processing and portfolio selection](https://mlsanity.com/paper/2304.08813/) (2023)
- [Bayesian Structure Learning in Undirected Gaussian Graphical Models: Literature Review with Empirical Comparison](https://mlsanity.com/paper/2307.02603/) (2023)
- [Online Change Detection in SAR Time-Series with Kronecker Product Structured Scaled Gaussian Models](https://mlsanity.com/paper/2312.02807/) (2023)

## Built on by (most cited first, 1 of 1)

- [Including Node Textual Metadata in Laplacian-constrained Gaussian Graphical Models](https://mlsanity.com/paper/2602.15920/) (2026)

## Abstract (arXiv)

This paper addresses the problem of learning an undirected graph from data gathered at each nodes. Within the graph signal processing framework, the topology of such graph can be linked to the support of the conditional correlation matrix of the data. The corresponding graph learning problem then scales to the squares of the number of variables (nodes), which is usually problematic at large dimension. To tackle this issue, we propose a graph learning framework that leverages a low-rank factorization of the conditional correlation matrix. In order to solve for the resulting optimization problems, we derive tools required to apply Riemannian optimization techniques for this particular structure. The proposal is then particularized to a low-rank constrained counterpart of the GLasso algorithm, i.e., the penalized maximum likelihood estimation of a Gaussian graphical model. Experiments on synthetic and real data evidence that a very efficient dimension-versus-performance trade-off can be achieved with this approach.