# Analyzing Dynamical Brain Functional Connectivity As Trajectories on Space of Covariance Matrices

arXiv: https://arxiv.org/abs/1904.05449 · HTML: https://mlsanity.com/paper/1904.05449/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Apr 2019.

## Built on by (most cited first, 9 of 9)

- [Tensor-CSPNet: A Novel Geometric Deep Learning Framework for Motor Imagery Classification](https://mlsanity.com/paper/2202.02472/) (2022)
- [Learning to Normalize on the SPD Manifold under Bures-Wasserstein Geometry](https://mlsanity.com/paper/2504.00660/) (2025)
- [SPD Matrix Learning for Neuroimaging Analysis: Perspectives, Methods, and Challenges](https://mlsanity.com/paper/2504.18882/) (2025)
- [Graph-Regularized Manifold-Aware Conditional Wasserstein GAN for Brain Functional Connectivity Generation](https://mlsanity.com/paper/2212.05316/) (2022)
- [Supervised deep learning of elastic SRV distances on the shape space of curves](https://mlsanity.com/paper/2101.04929/) (2021)
- [Riemannian Self-Attention Mechanism for SPD Networks](https://mlsanity.com/paper/2311.16738/) (2023)
- [Accounting for Temporal Variability in Functional Magnetic Resonance Imaging Improves Prediction of Intelligence](https://mlsanity.com/paper/2211.07429/) (2022)
- [Intrinsic Riemannian Cross-covariance for Manifold-valued Random Objects](https://mlsanity.com/paper/2606.10212/) (2026)
- [Geometric Feature Learning for Functional Data Valued on the Symmetric Positive Definite Manifold](https://mlsanity.com/paper/2609.30487/) (2026)

## Abstract (arXiv)

Human brain functional connectivity (FC) is often measured as the similarity of functional MRI responses across brain regions when a brain is either resting or performing a task. This paper aims to statistically analyze the dynamic nature of FC by representing the collective time-series data, over a set of brain regions, as a trajectory on the space of covariance matrices, or symmetric-positive definite matrices (SPDMs). We use a recently developed metric on the space of SPDMs for quantifying differences across FC observations, and for clustering and classification of FC trajectories. To facilitate large scale and high-dimensional data analysis, we propose a novel, metric-based dimensionality reduction technique to reduce data from large SPDMs to small SPDMs. We illustrate this comprehensive framework using data from the Human Connectome Project (HCP) database for multiple subjects and tasks, with task classification rates that match or outperform state-of-the-art techniques.