# Manifold-regression to predict from MEG/EEG brain signals without source modeling

arXiv: https://arxiv.org/abs/1906.02687 · HTML: https://mlsanity.com/paper/1906.02687/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jun 2019.

## Built on by (most cited first, 17 of 17)

- [SPD domain-specific batch normalization to crack interpretable unsupervised domain adaptation in EEG](https://mlsanity.com/paper/2206.01323/) (2022)
- [Tensor-CSPNet: A Novel Geometric Deep Learning Framework for Motor Imagery Classification](https://mlsanity.com/paper/2202.02472/) (2022)
- [Sliced-Wasserstein on Symmetric Positive Definite Matrices for M/EEG Signals](https://mlsanity.com/paper/2303.05798/) (2023)
- [Graph Neural Networks on SPD Manifolds for Motor Imagery Classification: A Perspective from the Time-Frequency Analysis](https://mlsanity.com/paper/2211.02641/) (2022)
- [Robust learning from corrupted EEG with dynamic spatial filtering](https://mlsanity.com/paper/2105.12916/) (2021)
- [Geodesic Optimization for Predictive Shift Adaptation on EEG data](https://mlsanity.com/paper/2407.03878/) (2024)
- [On the interpretation of linear Riemannian tangent space model parameters in M/EEG](https://mlsanity.com/paper/2107.14398/) (2021)
- [SPD Matrix Learning for Neuroimaging Analysis: Perspectives, Methods, and Challenges](https://mlsanity.com/paper/2504.18882/) (2025)
- [Classification of BCI-EEG based on augmented covariance matrix](https://mlsanity.com/paper/2302.04508/) (2023)
- [Multi-Tier Platform for Cognizing Massive Electroencephalogram](https://mlsanity.com/paper/2204.09840/) (2022)
- [Riemannian Geometry-Based EEG Approaches: A Literature Review](https://mlsanity.com/paper/2407.20250/) (2024)
- [SplitSEE: A Splittable Self-supervised Framework for Single-Channel EEG Representation Learning](https://mlsanity.com/paper/2410.11200/) (2024)
- [Weakly supervised covariance matrices alignment through Stiefel matrices estimation for MEG applications](https://mlsanity.com/paper/2402.03345/) (2024)
- [EEG-MACS: Manifold Attention and Confidence Stratification for EEG-based Cross-Center Brain Disease Diagnosis under Unreliable Annotations](https://mlsanity.com/paper/2405.00734/) (2024)
- [Persistent Homological State-Space Estimation of Functional Human Brain Networks at Rest](https://mlsanity.com/paper/2201.00087/) (2022)
- [Brain Age Revisited: Investigating the State vs. Trait Hypotheses of EEG-derived Brain-Age Dynamics with Deep Learning](https://mlsanity.com/paper/2310.07029/) (2023)
- [NeurDuo-EEG: A Long-Sequence EEG Foundation Model with Persistent State and Explicit Memory](https://mlsanity.com/paper/2609.38587/) (2026)

## Abstract (arXiv)

Magnetoencephalography and electroencephalography (M/EEG) can reveal neuronal dynamics non-invasively in real-time and are therefore appreciated methods in medicine and neuroscience. Recent advances in modeling brain-behavior relationships have highlighted the effectiveness of Riemannian geometry for summarizing the spatially correlated time-series from M/EEG in terms of their covariance. However, after artefact-suppression, M/EEG data is often rank deficient which limits the application of Riemannian concepts. In this article, we focus on the task of regression with rank-reduced covariance matrices. We study two Riemannian approaches that vectorize the M/EEG covariance between-sensors through projection into a tangent space. The Wasserstein distance readily applies to rank-reduced data but lacks affine-invariance. This can be overcome by finding a common subspace in which the covariance matrices are full rank, enabling the affine-invariant geometric distance. We investigated the implications of these two approaches in synthetic generative models, which allowed us to control estimation bias of a linear model for prediction. We show that Wasserstein and geometric distances allow perfect out-of-sample prediction on the generative models. We then evaluated the methods on real data with regard to their effectiveness in predicting age from M/EEG covariance matrices. The findings suggest that the data-driven Riemannian methods outperform different sensor-space estimators and that they get close to the performance of biophysics-driven source-localization model that requires MRI acquisitions and tedious data processing. Our study suggests that the proposed Riemannian methods can serve as fundamental building-blocks for automated large-scale analysis of M/EEG.