# Geometric Neural Network based on Phase Space for BCI-EEG decoding

arXiv: https://arxiv.org/abs/2403.05645 · HTML: https://mlsanity.com/paper/2403.05645/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 106 references that are in the map.
- First posted on arXiv 8 Mar 2024.

## Builds on (most cited first, 30 of 31)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Grad-CAM++: Improved Visual Explanations for Deep Convolutional Networks](https://mlsanity.com/paper/1710.11063/) (2017)
- [EEGNet: A Compact Convolutional Network for EEG-based Brain-Computer Interfaces](https://mlsanity.com/paper/1611.08024/) (2016)
- [Riemannian Adaptive Optimization Methods](https://mlsanity.com/paper/1810.00760/) (2018)
- [A Riemannian Network for SPD Matrix Learning](https://mlsanity.com/paper/1608.04233/) (2016)
- [Deep learning-based electroencephalography analysis: a systematic review](https://mlsanity.com/paper/1901.05498/) (2019)
- [Tree-Structured Parzen Estimator: Understanding Its Algorithm Components and Their Roles for Better Empirical Performance](https://mlsanity.com/paper/2304.11127/) (2023)
- [Geoopt: Riemannian Optimization in PyTorch](https://mlsanity.com/paper/2005.02819/) (2020)
- [MOABB: Trustworthy algorithm benchmarking for BCIs](https://mlsanity.com/paper/1805.06427/) (2018)
- [Riemannian batch normalization for SPD neural networks](https://mlsanity.com/paper/1909.02414/) (2019)
- [Brain decoding: toward real-time reconstruction of visual perception](https://mlsanity.com/paper/2310.19812/) (2023)
- [EEG-TCNet: An Accurate Temporal Convolutional Network for Embedded Motor-Imagery Brain-Machine Interfaces](https://mlsanity.com/paper/2006.00622/) (2020)
- [Diffusion Models for Constrained Domains](https://mlsanity.com/paper/2304.05364/) (2023)
- [SPD domain-specific batch normalization to crack interpretable unsupervised domain adaptation in EEG](https://mlsanity.com/paper/2206.01323/) (2022)
- [MAtt: A Manifold Attention Network for EEG Decoding](https://mlsanity.com/paper/2210.01986/) (2022)
- [Federated Transfer Learning for EEG Signal Classification](https://mlsanity.com/paper/2004.12321/) (2020)
- [Data augmentation for learning predictive models on EEG: a systematic comparison](https://mlsanity.com/paper/2206.14483/) (2022)
- [CADDA: Class-wise Automatic Differentiable Data Augmentation for EEG Signals](https://mlsanity.com/paper/2106.13695/) (2021)
- [Tensor-CSPNet: A Novel Geometric Deep Learning Framework for Motor Imagery Classification](https://mlsanity.com/paper/2202.02472/) (2022)
- [Toward reliable signals decoding for electroencephalogram: A benchmark study to EEGNeX](https://mlsanity.com/paper/2207.12369/) (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)
- [Robust learning from corrupted EEG with dynamic spatial filtering](https://mlsanity.com/paper/2105.12916/) (2021)
- [SPD-DDPM: Denoising Diffusion Probabilistic Models in the Symmetric Positive Definite Space](https://mlsanity.com/paper/2312.08200/) (2023)
- [EEG-ITNet: An Explainable Inception Temporal Convolutional Network for Motor Imagery Classification](https://mlsanity.com/paper/2204.06947/) (2022)
- [EEG motor imagery decoding: A framework for comparative analysis with channel attention mechanisms](https://mlsanity.com/paper/2310.11198/) (2023)
- [Faster ICA under orthogonal constraint](https://mlsanity.com/paper/1711.10873/) (2017)
- [Unifying Pairwise Interactions in Complex Dynamics](https://mlsanity.com/paper/2201.11941/) (2022)
- [Functional connectivity ensemble method to enhance BCI performance (FUCONE)](https://mlsanity.com/paper/2111.03122/) (2021)
- [Classification of BCI-EEG based on augmented covariance matrix](https://mlsanity.com/paper/2302.04508/) (2023)

## Built on by (most cited first, 5 of 5)

- [Riemannian Geometry-Based EEG Approaches: A Literature Review](https://mlsanity.com/paper/2407.20250/) (2024)
- [SPD Learn: A Geometric Deep Learning Python Library for Neural Decoding Through Trivialization](https://mlsanity.com/paper/2602.22895/) (2026)
- [FedSPDnet: Geometry-Aware Federated Deep Learning with SPDnet](https://mlsanity.com/paper/2604.22494/) (2026)
- [Escaping the Capacity Ceiling: Routing on the Stiefel Manifold for Bilinear SPD Layers](https://mlsanity.com/paper/2605.31043/) (2026)
- [Personalised federated learning for Riemannian and Euclidean EEG decoding](https://mlsanity.com/paper/2609.29037/) (2026)

## Abstract (arXiv)

Objective: The integration of Deep Learning (DL) algorithms on brain signal analysis is still in its nascent stages compared to their success in fields like Computer Vision. This is particularly true for BCI, where the brain activity is decoded to control external devices without requiring muscle control. Electroencephalography (EEG) is a widely adopted choice for designing BCI systems due to its non-invasive and cost-effective nature and excellent temporal resolution. Still, it comes at the expense of limited training data, poor signal-to-noise, and a large variability across and within-subject recordings. Finally, setting up a BCI system with many electrodes takes a long time, hindering the widespread adoption of reliable DL architectures in BCIs outside research laboratories. To improve adoption, we need to improve user comfort using, for instance, reliable algorithms that operate with few electrodes. Approach: Our research aims to develop a DL algorithm that delivers effective results with a limited number of electrodes. Taking advantage of the Augmented Covariance Method and the framework of SPDNet, we propose the Phase-SPDNet architecture and analyze its performance and the interpretability of the results. The evaluation is conducted on 5-fold cross-validation, using only three electrodes positioned above the Motor Cortex. The methodology was tested on nearly 100 subjects from several open-source datasets using the Mother Of All BCI Benchmark (MOABB) framework. Main results: The results of our Phase-SPDNet demonstrate that the augmented approach combined with the SPDNet significantly outperforms all the current state-of-the-art DL architecture in MI decoding. Significance: This new architecture is explainable and with a low number of trainable parameters.