# Riemannian Geometry-Based EEG Approaches: A Literature Review

arXiv: https://arxiv.org/abs/2407.20250 · HTML: https://mlsanity.com/paper/2407.20250/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 115 references that are in the map.
- First posted on arXiv 19 Jul 2024.

## Builds on (most cited first, 15 of 15)

- [A Riemannian Network for SPD Matrix Learning](https://mlsanity.com/paper/1608.04233/) (2016)
- [CSP: Self-Supervised Contrastive Spatial Pre-Training for Geospatial-Visual Representations](https://mlsanity.com/paper/2305.01118/) (2023)
- [MAtt: A Manifold Attention Network for EEG Decoding](https://mlsanity.com/paper/2210.01986/) (2022)
- [Manifold-regression to predict from MEG/EEG brain signals without source modeling](https://mlsanity.com/paper/1906.02687/) (2019)
- [Graph Neural Networks on SPD Manifolds for Motor Imagery Classification: A Perspective from the Time-Frequency Analysis](https://mlsanity.com/paper/2211.02641/) (2022)
- [Deep Riemannian Networks for End-to-End EEG Decoding](https://mlsanity.com/paper/2212.10426/) (2022)
- [A Survey on Deep Learning-based Non-Invasive Brain Signals:Recent Advances and New Frontiers](https://mlsanity.com/paper/1905.04149/) (2019)
- [R-Mixup: Riemannian Mixup for Biological Networks](https://mlsanity.com/paper/2306.02532/) (2023)
- [Spatio-Temporal EEG Representation Learning on Riemannian Manifold and Euclidean Space](https://mlsanity.com/paper/2008.08633/) (2020)
- [Geometric Neural Network based on Phase Space for BCI-EEG decoding](https://mlsanity.com/paper/2403.05645/) (2024)
- [Riemannian classification of EEG signals with missing values](https://mlsanity.com/paper/2110.10011/) (2021)
- [Riemannian geometry applied to detection of respiratory states from EEG signals: the basis for a brain-ventilator interface](https://mlsanity.com/paper/1601.03022/) (2016)
- [EEG Representation Using Multi-instance Framework on The Manifold of Symmetric Positive Definite Matrices for EEG-based Computer Aided Diagnosis](https://mlsanity.com/paper/1702.02655/) (2017)
- [Towards identifying optimal biased feedback for various user states and traits in motor imagery BCI](https://mlsanity.com/paper/2112.12399/) (2021)
- [Manifold GCN: Diffusion-based Convolutional Neural Network for Manifold-valued Graphs](https://mlsanity.com/paper/2401.14381/) (2024)

## Built on by (most cited first, 3 of 3)

- [MPEC: Manifold-Preserved EEG Classification via an Ensemble of Clustering-Based Classifiers](https://mlsanity.com/paper/2504.21427/) (2025)
- [Quantity versus Diversity: Influence of Data on Detecting EEG Pathology with Advanced ML Models](https://mlsanity.com/paper/2411.17709/) (2024)
- [Riemannian geometry meets fMRI: the advantages of modeling correlation manifolds and eigenvector subspaces](https://mlsanity.com/paper/2605.22334/) (2026)

## Abstract (arXiv)

The application of Riemannian geometry in the decoding of brain-computer interfaces (BCIs) has swiftly garnered attention because of its straightforwardness, precision, and resilience, along with its aptitude for transfer learning, which has been demonstrated through significant achievements in global BCI competitions. This paper presents a comprehensive review of recent advancements in the integration of deep learning with Riemannian geometry to enhance EEG signal decoding in BCIs. Our review updates the findings since the last major review in 2017, comparing modern approaches that utilize deep learning to improve the handling of non-Euclidean data structures inherent in EEG signals. We discuss how these approaches not only tackle the traditional challenges of noise sensitivity, non-stationarity, and lengthy calibration times but also introduce novel classification frameworks and signal processing techniques to reduce these limitations significantly. Furthermore, we identify current shortcomings and propose future research directions in manifold learning and riemannian-based classification, focusing on practical implementations and theoretical expansions, such as feature tracking on manifolds, multitask learning, feature extraction, and transfer learning. This review aims to bridge the gap between theoretical research and practical, real-world applications, making sophisticated mathematical approaches accessible and actionable for BCI enhancements.