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LGL-BCI: A Motor-Imagery-Based Brain-Computer Interface with Geometric Learning

Jianchao Lu, Yuzhe Tian, Yang Zhang, Quan Z. Sheng, Xi Zheng

TL;DR

This paper tackles the challenges of EEG-based motor imagery BCIs, notably amplitude/phase variability and non-Euclidean spatial correlations, by introducing LGL-BCI, a lightweight geometric learning framework operating on SPD manifolds. The approach combines SPD manifold construction, geometry-aware channel selection, a lossless tangent-space transformation, and a tangent-space CNN with a multi-head bilinear transformation to achieve high accuracy with far fewer parameters than state-of-the-art methods. Key contributions include first applying geometric deep learning to real-world consumer EEG devices for MI-BCIs, a geometry-driven channel selection mechanism with MBT, and extensive validation showing 82.54% real-world accuracy with 64.9K parameters and faster inference than comparable models. The proposed method enables practical, real-time MI-BCI deployment on mobile hardware and highlights the potential of geometric DL to improve robustness and efficiency in non-Euclidean EEG data processing.

Abstract

Brain--computer interfaces are groundbreaking technology whereby brain signals are used to control external devices. Despite some advances in recent years, electroencephalogram (EEG)-based motor-imagery tasks face challenges, such as amplitude and phase variability and complex spatial correlations, with a need for smaller models and faster inference. In this study, we develop a prototype, called the Lightweight Geometric Learning Brain--Computer Interface (LGL-BCI), which uses our customized geometric deep learning architecture for swift model inference without sacrificing accuracy. LGL-BCI contains an EEG channel selection module via a feature decomposition algorithm to reduce the dimensionality of a symmetric positive definite matrix, providing adaptiveness among the continuously changing EEG signal. Meanwhile, a built-in lossless transformation helps boost the inference speed. The performance of our solution was evaluated using two real-world EEG devices and two public EEG datasets. LGL-BCI demonstrated significant improvements, achieving an accuracy of 82.54% compared to 62.22% for the state-of-the-art approach. Furthermore, LGL-BCI uses fewer parameters (64.9K vs. 183.7K), highlighting its computational efficiency. These findings underscore both the superior accuracy and computational efficiency of LGL-BCI, demonstrating the feasibility and robustness of geometric deep learning in motor-imagery brain--computer interface applications.

LGL-BCI: A Motor-Imagery-Based Brain-Computer Interface with Geometric Learning

TL;DR

This paper tackles the challenges of EEG-based motor imagery BCIs, notably amplitude/phase variability and non-Euclidean spatial correlations, by introducing LGL-BCI, a lightweight geometric learning framework operating on SPD manifolds. The approach combines SPD manifold construction, geometry-aware channel selection, a lossless tangent-space transformation, and a tangent-space CNN with a multi-head bilinear transformation to achieve high accuracy with far fewer parameters than state-of-the-art methods. Key contributions include first applying geometric deep learning to real-world consumer EEG devices for MI-BCIs, a geometry-driven channel selection mechanism with MBT, and extensive validation showing 82.54% real-world accuracy with 64.9K parameters and faster inference than comparable models. The proposed method enables practical, real-time MI-BCI deployment on mobile hardware and highlights the potential of geometric DL to improve robustness and efficiency in non-Euclidean EEG data processing.

Abstract

Brain--computer interfaces are groundbreaking technology whereby brain signals are used to control external devices. Despite some advances in recent years, electroencephalogram (EEG)-based motor-imagery tasks face challenges, such as amplitude and phase variability and complex spatial correlations, with a need for smaller models and faster inference. In this study, we develop a prototype, called the Lightweight Geometric Learning Brain--Computer Interface (LGL-BCI), which uses our customized geometric deep learning architecture for swift model inference without sacrificing accuracy. LGL-BCI contains an EEG channel selection module via a feature decomposition algorithm to reduce the dimensionality of a symmetric positive definite matrix, providing adaptiveness among the continuously changing EEG signal. Meanwhile, a built-in lossless transformation helps boost the inference speed. The performance of our solution was evaluated using two real-world EEG devices and two public EEG datasets. LGL-BCI demonstrated significant improvements, achieving an accuracy of 82.54% compared to 62.22% for the state-of-the-art approach. Furthermore, LGL-BCI uses fewer parameters (64.9K vs. 183.7K), highlighting its computational efficiency. These findings underscore both the superior accuracy and computational efficiency of LGL-BCI, demonstrating the feasibility and robustness of geometric deep learning in motor-imagery brain--computer interface applications.
Paper Structure (40 sections, 2 theorems, 29 equations, 8 figures, 7 tables)

This paper contains 40 sections, 2 theorems, 29 equations, 8 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Motivations
  3. Empowering Disabilities with EEG Real-World Deployment
  4. EEG-Controlled Mobility Assistance Devices
  5. Problems with Current EEG Devices
  6. Geometric Deep Learning and Current Implementation in MI-BCIs
  7. Insights
  8. Related Work
  9. Geometric Deep Learning in MI-BCIs
  10. Other Methods in MI-BCIs
  11. The LGL-BCI Approach
  12. Architecture
  13. SPD Manifold Construction Module
  14. SPD Manifold Operation Module: Feature Extraction
  15. SPD Manifold Operation Module: Channel Selection
  16. ...and 25 more sections

Key Result

Theorem 1

If we let $A = (-\frac{1}{2}(G^{2}-D^{2}))$, then $HAH$ results in a positive semi-definite (p.s.d.) matrix, with $H=I_{m}-m^{-1}11^{T}$ representing the centering matrix. Here, $1=[1, 1, \dots, 1]^{T} \in \mathbb{R}^{m}$, and $I_{m}$ is an $m \times m$ identity matrix.

Figures (8)

  • Figure 1: Architectural overview of LGL-BCI
  • Figure 2: Photos of different hardware sets
  • Figure 3: Images signifying motor-imagery tasks
  • Figure 4: Evaluating the performance differential across various channels selected in the one- and four-head settings
  • Figure 5: Significance heatmap of frequency bands across four MI tasks
  • ...and 3 more figures

Theorems & Definitions (2)

  • Theorem 1
  • Theorem 2