[Paper Review] Deep Riemannian Networks for End-to-End EEG Decoding

Daniel J. Wilson, Robin Tibor Schirrmeister+2 more|arXiv (Cornell University)|Dec 20, 2022

EEG and Brain-Computer Interfaces10 citations

TL;DR

This paper proposes EE(G)-SPDNet, a novel end-to-end Deep Riemannian Network for EEG decoding that learns optimal frequency filters directly from raw EEG data using a convolutional layer within an SPD (symmetric positive definite) matrix framework. The model achieves state-of-the-art performance on public EEG datasets by learning physiologically plausible frequency bands and outperforming both standard ConvNets and traditional filterbank-based methods, while revealing that Riemannian-specific information may be lost in deeper layers.

ABSTRACT

State-of-the-art performance in electroencephalography (EEG) decoding tasks is currently often achieved with either Deep-Learning (DL) or Riemannian-Geometry-based decoders (RBDs). Recently, there is growing interest in Deep Riemannian Networks (DRNs) possibly combining the advantages of both previous classes of methods. However, there are still a range of topics where additional insight is needed to pave the way for a more widespread application of DRNs in EEG. These include architecture design questions such as network size and end-to-end ability. How these factors affect model performance has not been explored. Additionally, it is not clear how the data within these networks is transformed, and whether this would correlate with traditional EEG decoding. Our study aims to lay the groundwork in the area of these topics through the analysis of DRNs for EEG with a wide range of hyperparameters. Networks were tested on five public EEG datasets and compared with state-of-the-art ConvNets. Here we propose EE(G)-SPDNet, and we show that this wide, end-to-end DRN can outperform the ConvNets, and in doing so use physiologically plausible frequency regions. We also show that the end-to-end approach learns more complex filters than traditional band-pass filters targeting the classical alpha, beta, and gamma frequency bands of the EEG, and that performance can benefit from channel specific filtering approaches. Additionally, architectural analysis revealed areas for further improvement due to the possible under utilisation of Riemannian specific information throughout the network. Our study thus shows how to design and train DRNs to infer task-related information from the raw EEG without the need of handcrafted filterbanks and highlights the potential of end-to-end DRNs such as EE(G)-SPDNet for high-performance EEG decoding.

Motivation & Objective

• To develop an end-to-end Deep Riemannian Network (DRN) that bypasses handcrafted filterbanks for EEG decoding.
• To investigate how architectural choices such as network depth and width affect performance in DRNs for EEG.
• To analyze whether end-to-end DRNs learn more complex, physiologically plausible frequency filters than classical band-pass filters.
• To evaluate the impact of Riemannian geometry on feature representation and classification performance.
• To identify architectural limitations, such as potential loss of Riemannian-specific information during feature transformation.

Proposed method

• Proposes EE(G)-SPDNet, a wide, end-to-end DRN that integrates a learnable convolutional layer for frequency filterbank learning directly within an SPD matrix framework.
• Employs a Bayesian optimisation (BO) strategy to search hyperparameters, including filterbank design, to improve model performance.
• Uses symmetric positive definite (SPD) matrices derived from EEG covariance to represent multivariate brain signals in a Riemannian manifold.
• Applies Riemannian metrics such as the Log-Euclidean and Affine-Invariant Riemannian metrics to compute distances and transformations in the SPD space.
• Performs layer-by-layer (LBL) analysis to visualize how data is transformed through the network and assess feature learning.
• Compares the end-to-end model with traditional Riemannian and Euclidean classifiers (e.g., rSVM, SVM) to evaluate the specificity of learned features.

Experimental results

Research questions

• RQ1 Can an end-to-end Deep Riemannian Network learn optimal, physiologically plausible frequency filters for EEG decoding without handcrafted filterbanks?
• RQ2 How does the depth and width of a DRN architecture affect classification performance on EEG data?
• RQ3 Does the end-to-end learning process in DRNs produce filters that align with classical EEG frequency bands (e.g., alpha, beta, gamma)?
• RQ4 To what extent are Riemannian-specific features preserved through the network, and where might information be lost?
• RQ5 Can Bayesian optimisation effectively search the high-dimensional space of filterbank and network hyperparameters to improve EEG decoding accuracy?

Key findings

• EE(G)-SPDNet achieved statistically significant performance gains over state-of-the-art models such as Deep4Net and ShallowFBCSPNet on public EEG datasets.
• The model learned frequency filters that correspond to physiologically relevant EEG bands, such as alpha and beta, demonstrating biological plausibility.
• End-to-end training enabled the network to learn complex, non-linear filter responses that go beyond classical band-pass filtering.
• Layer-by-layer analysis revealed that deeper layers may lose Riemannian-specific information, suggesting a need for architectural refinement.
• The performance of the rSVM classifier decreased in deeper layers, indicating that Riemannian transformations are not always optimally preserved through the network.
• Bayesian optimisation successfully identified high-performing architectures, and the resulting BO-SPDNet model demonstrated robust generalisation across datasets.