# Multi-Scale Factor Analysis of High-Dimensional Brain Signals

## TL;DR

This paper introduces a multi-scale factor analysis method for modeling high-dimensional brain networks, capturing regional and global dependencies efficiently, and revealing hierarchical brain organization from fMRI data.

## Contribution

The novel MSFA model partitions complex networks into clusters, reduces dimensionality with latent factors, and estimates connectivity at multiple scales using PCA and RV-coefficient.

## Key findings

- Revealed modular and hierarchical brain organization during rest.
- Provided a computationally efficient approach for large network analysis.
- Applied to fMRI data to uncover brain connectivity patterns.

## Abstract

In this paper, we develop an approach to modeling high-dimensional networks with a large number of nodes arranged in a hierarchical and modular structure. We propose a novel multi-scale factor analysis (MSFA) model which partitions the massive spatio-temporal data defined over the complex networks into a finite set of regional clusters. To achieve further dimension reduction, we represent the signals in each cluster by a small number of latent factors. The correlation matrix for all nodes in the network are approximated by lower-dimensional sub-structures derived from the cluster-specific factors. To estimate regional connectivity between numerous nodes (within each cluster), we apply principal components analysis (PCA) to produce factors which are derived as the optimal reconstruction of the observed signals under the squared loss. Then, we estimate global connectivity (between clusters or sub-networks) based on the factors across regions using the RV-coefficient as the cross-dependence measure. This gives a reliable and computationally efficient multi-scale analysis of both regional and global dependencies of the large networks. The proposed novel approach is applied to estimate brain connectivity networks using functional magnetic resonance imaging (fMRI) data. Results on resting-state fMRI reveal interesting modular and hierarchical organization of human brain networks during rest.