Sparse covariate-driven factorization of high-dimensional brain connectivity with application to site effect correction

TL;DR

SLACC addresses the problem of site effects in multi-site brain connectivity by introducing a covariate-driven, sparse latent-factor decomposition of symmetric connectivity matrices. It models each subject's connectivity as a sum of sparse rank-1 patterns weighted by covariate-dependent scores, with site-specific mean and variance effects captured through a penalized EM framework and ADMM-based updates. An extended BIC guides the latent-dimension choice, and a harmonization procedure removes site-driven heterogeneity while preserving biological variation. Applied to ABIDE rs-fMRI data and validated in simulations, SLACC reduces site effects more effectively on variances while maintaining meaningful covariate associations, and it is implemented in an R package for public use.

Abstract

Large-scale neuroimaging studies often collect data from multiple scanners across different sites, where variations in scanners, scanning procedures, and other conditions across sites can introduce artificial site effects. These effects may bias brain connectivity measures, such as functional connectivity (FC), which quantify functional network organization derived from functional magnetic resonance imaging (fMRI). How to leverage high-dimensional network structures to effectively mitigate site effects has yet to be addressed. In this paper, we propose SLACC (Sparse LAtent Covariate-driven Connectome) factorization, a multivariate method that explicitly parameterizes covariate effects in latent subject scores corresponding to sparse rank-1 latent patterns derived from brain connectivity. The proposed method identifies localized site-driven variability within and across brain networks, enabling targeted correction. We develop a penalized Expectation-Maximization (EM) algorithm for parameter estimation, incorporating the Bayesian Information Criterion (BIC) to guide optimization. Extensive simulations validate SLACC's robustness in recovering the true parameters and underlying connectivity patterns. Applied to the Autism Brain Imaging Data Exchange (ABIDE) dataset, SLACC demonstrates its ability to reduce site effects. The R package to implement our method is publicly available.

Figures (6)

• Figure 1: Illustration of framework decomposing a subject's connectivity matrix into sparse rank-1 connectivity patterns $\{ {\bf u} _l {\bf u} _l^\top\}_{l=1}^L$, weighted by subject scores $a_{ijl}$ modeled by covariates ${\bf x} _{ij}$.
• Figure 2: True ${\bf U} \in\mathbb{R}^{50\times 5}$ for scenarios 1 and 2 used in simulation studies.
• Figure 3: Results of Simulation 1. The left and right columns describe scenarios 1 and 2, respectively. The first 4 rows describe MSE (red+blue), bias$^2$ (red) and variance (blue). The last row shows sensitivity and specificity of the estimated ${\bf U}$.
• Figure 4: Estimated ${ {\bf U} }$ ($L=73$) using the training data ($n=591$), with the column orders obtained by hierarchical clustering.
• Figure 5: $F$ test statistic for measuring mean and variance heterogeneity across sites, using both training (first row) and test data (second row). The dotted horizontal line is the expected value of the null $F$ distribution (i.e., no site effects). The solid line is the 45 degree line.

Theorems & Definitions (1)

• Theorem 1