[Paper Review] MAtt: A Manifold Attention Network for EEG Decoding

Yueting Pan, Jing-Lun Chou+1 more|arXiv (Cornell University)|Oct 5, 2022

EEG and Brain-Computer Interfaces25 citations

TL;DR

MAtt is a geometric deep learning model that maps EEG features to a SPD manifold and uses a manifold attention mechanism to improve decoding across time-synchronous and time-asynchronous EEG tasks.

ABSTRACT

Recognition of electroencephalographic (EEG) signals highly affect the efficiency of non-invasive brain-computer interfaces (BCIs). While recent advances of deep-learning (DL)-based EEG decoders offer improved performances, the development of geometric learning (GL) has attracted much attention for offering exceptional robustness in decoding noisy EEG data. However, there is a lack of studies on the merged use of deep neural networks (DNNs) and geometric learning for EEG decoding. We herein propose a manifold attention network (mAtt), a novel geometric deep learning (GDL)-based model, featuring a manifold attention mechanism that characterizes spatiotemporal representations of EEG data fully on a Riemannian symmetric positive definite (SPD) manifold. The evaluation of the proposed MAtt on both time-synchronous and -asyncronous EEG datasets suggests its superiority over other leading DL methods for general EEG decoding. Furthermore, analysis of model interpretation reveals the capability of MAtt in capturing informative EEG features and handling the non-stationarity of brain dynamics.

Motivation & Objective

• Motivate robust EEG decoding under non-stationarity and noise using geometric deep learning.
• Propose a lightweight framework that integrates Euclidean and Riemannian representations of EEG features.
• Develop a manifold attention mechanism operating on SPD matrices to capture spatiotemporal patterns.
• Validate generalization across time-synchronous and time-asynchronous EEG datasets.

Proposed method

• Extract EEG features via two convolutional layers for spatial and spatiotemporal representation.
• Convert Euclidean embeddings into SPD matrices for Riemannian processing using Log-Euclidean metrics.
• Implement a manifold attention module that uses bilinear mappings to produce SPD queries, keys, and values.
• Compute similarity between SPD queries/keys via Log-Euclidean distance and apply Softmax-based attention on the SPD manifold.
• Fuse attended SPD values via Log-Euclidean mean and map back to Euclidean space with ReEig and Log layers for classification.
• Train with cross-entropy loss using Stiefel-manifold gradient updates to keep transformation matrices on the Stiefel manifold.

Experimental results

Research questions

• RQ1 Can the proposed MAtt framework improve EEG decoding accuracy across MI (time-asynchronous), SSVEP (time-synchronous), and ERN datasets compared to leading DL methods?
• RQ2 Does integrating Euclidean and Riemannian representations via a manifold attention mechanism yield better generalization and interpretability for EEG signals?
• RQ3 How does the model handle non-stationarity and variability across subjects and sessions?
• RQ4 What is the contribution of the manifold attention module versus the feature extractor in overall performance?

Key findings

• MAtt outperforms baseline DL methods on MI, SSVEP, and ERN datasets in the reported experiments.
• FE+MA (proposed) achieves the best accuracy across all three tasks, outperforming FE alone and FE+Self-Attention alternatives.
• Across MI, SSVEP, and ERN, MAtt demonstrates robust generalization and interpretable feature capture via gradient-based localization.
• Ablation shows that combining feature extraction with the manifold attention module yields the strongest performance.
• Model interpretation reveals spatial patterns consistent with motor cortex activity and mu-band timing in EEG signals.