Clustering Gaussian Graphical Models

TL;DR

This paper introduces a novel method for clustering nodes in Gaussian graphical models directly from data, utilizing partial correlations and matrix factorization to handle limited data scenarios, demonstrated on fMRI data.

Contribution

The paper presents an efficient clustering technique for Gaussian graphical models that avoids estimating the full covariance matrix, suitable for limited data situations.

Findings

Effective clustering of nodes based on network neighborhoods

Applicable to limited data scenarios with rank-deficient covariance matrices

Validated on Human Connectome Project fMRI data

Abstract

We derive an efficient method to perform clustering of nodes in Gaussian graphical models directly from sample data. Nodes are clustered based on the similarity of their network neighborhoods, with edge weights defined by partial correlations. In the limited-data scenario, where the covariance matrix would be rank-deficient, we are able to make use of matrix factors, and never need to estimate the actual covariance or precision matrix. We demonstrate the method on functional MRI data from the Human Connectome Project. A matlab implementation of the algorithm is provided.