# On the interpretation of linear Riemannian tangent space model parameters in M/EEG

arXiv: https://arxiv.org/abs/2107.14398 · HTML: https://mlsanity.com/paper/2107.14398/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 23 references that are in the map.
- First posted on arXiv 30 Jul 2021.

## Builds on (most cited first, 3 of 3)

- [Machine-Learning-Based Diagnostics of EEG Pathology](https://mlsanity.com/paper/2002.05115/) (2020)
- [Manifold-regression to predict from MEG/EEG brain signals without source modeling](https://mlsanity.com/paper/1906.02687/) (2019)
- [Tangent space spatial filters for interpretable and efficient Riemannian classification](https://mlsanity.com/paper/1909.10567/) (2019)

## Built on by (most cited first, 8 of 8)

- [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)
- [Graph Neural Networks on SPD Manifolds for Motor Imagery Classification: A Perspective from the Time-Frequency Analysis](https://mlsanity.com/paper/2211.02641/) (2022)
- [SPDIM: Source-Free Unsupervised Conditional and Label Shift Adaptation in EEG](https://mlsanity.com/paper/2411.07249/) (2024)
- [Deep Optimal Transport for Domain Adaptation on SPD Manifolds](https://mlsanity.com/paper/2201.05745/) (2022)
- [SPD Matrix Learning for Neuroimaging Analysis: Perspectives, Methods, and Challenges](https://mlsanity.com/paper/2504.18882/) (2025)
- [Explainable artificial intelligence approaches for brain-computer interfaces: a review and design space](https://mlsanity.com/paper/2312.13033/) (2023)
- [Rectifying Geometric Misalignment: Online Source-Free Adaptation for Class-Imbalanced EEG](https://mlsanity.com/paper/2608.05315/) (2026)

## Abstract (arXiv)

Riemannian tangent space methods offer state-of-the-art performance in magnetoencephalography (MEG) and electroencephalography (EEG) based applications such as brain-computer interfaces and biomarker development. One limitation, particularly relevant for biomarker development, is limited model interpretability compared to established component-based methods. Here, we propose a method to transform the parameters of linear tangent space models into interpretable patterns. Using typical assumptions, we show that this approach identifies the true patterns of latent sources, encoding a target signal. In simulations and two real MEG and EEG datasets, we demonstrate the validity of the proposed approach and investigate its behavior when the model assumptions are violated. Our results confirm that Riemannian tangent space methods are robust to differences in the source patterns across observations. We found that this robustness property also transfers to the associated patterns.