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GCNs-Net: A Graph Convolutional Neural Network Approach for Decoding Time-resolved EEG Motor Imagery Signals
Yimin Hou, Shuyue Jia, Xiangmin Lun, Ziqian Hao, Yan Shi, Yang Li, Rui Zeng, Jinglei Lv
TL;DR
EEG MI decoding needs models that account for functional relationships among electrodes rather than relying only on Euclidean structure. This paper builds GCNs-Net from absolute-PCC graph Laplacians, graph convolutions, pooling, and softmax prediction, achieving strong subject- and group-level results across two datasets. The method also shows reproducible cross-validation performance and is presented as a framework for decoding relevant motor-imagery features.
Problem
Traditional EEG classifiers do not consider electrode topology, although brain dynamics exhibit network patterns that may not be reflected by Euclidean electrode structure.
Method
GCNs-Net builds an electrode graph from the absolute Pearson correlation matrix, learns features with graph convolutions, reduces dimensionality by pooling, and predicts MI classes with a fully connected softmax layer.
Results
Across PhysioNet and High Gamma, GCNs-Net achieves averaged accuracies of 93.06% and 96.24% at the subject level, and 88.57% and 80.89% at the group level, respectively.
Takeaways & Limitations
The framework decodes time-resolved EEG MI signals while cooperating with functional electrode topology and converges for both personalized and group-wise predictions.
Abstract
from arXiv · showhide
Towards developing effective and efficient brain-computer interface (BCI) systems, precise decoding of brain activity measured by electroencephalogram (EEG), is highly demanded. Traditional works classify EEG signals without considering the topological relationship among electrodes. However, neuroscience research has increasingly emphasized network patterns of brain dynamics. Thus, the Euclidean structure of electrodes might not adequately reflect the interaction between signals. To fill the gap, a novel deep learning framework based on the graph convolutional neural networks (GCNs) is presented to enhance the decoding performance of raw EEG signals during different types of motor imagery (MI) tasks while cooperating with the functional topological relationship of electrodes. Based on the absolute Pearson's matrix of overall signals, the graph Laplacian of EEG electrodes is built up. The GCNs-Net constructed by graph convolutional layers learns the generalized features. The followed pooling layers reduce dimensionality, and the fully-connected softmax layer derives the final prediction. The introduced approach has been shown to converge for both personalized and group-wise predictions. It has achieved the highest averaged accuracy, 93.06% and 88.57% (PhysioNet Dataset), 96.24% and 80.89% (High Gamma Dataset), at the subject and group level, respectively, compared with existing studies, which suggests adaptability and robustness to individual variability. Moreover, the performance is stably reproducible among repetitive experiments for cross-validation. The excellent performance of our method has shown that it is an important step towards better BCI approaches. To conclude, the GCNs-Net filters EEG signals based on the functional topological relationship, which manages to decode relevant features for brain motor imagery.
I. INTRODUCTION
EEG-based BCI research seeks to decode motor-imagery brain activity, but conventional approaches often overlook electrode topology. GCNs-Net addresses this gap by combining graph-based electrode relationships with deep learning for EEG MI decoding.
- EEG supports noninvasive, portable BCI systems that decode motor-imagery patterns for controlling assistive devices.
- Traditional EEG studies manually engineer features or apply CNNs to Euclidean-structured signals, without directly modeling electrode topology.
- GCNs-Net represents electrode relationships through a graph and uses graph convolutional layers, pooling, and a fully connected softmax layer to decode EEG MI signals.
- The framework targets four-class MI intentions and reports individual and group-wise performance exceeding existing studies on two benchmark datasets.
A. Overview
The framework combines raw multichannel EEG with a graph representation of electrode correlations before applying GCNs-Net for MI decoding. Its evaluation uses two benchmark datasets and time-resolved samples to assess effectiveness, robustness, and stability.
- The system acquires 64-channel raw EEG signals and constructs graph information from PCC, absolute PCC, adjacency, and Laplacian representations.
- GCNs-Net decodes EEG MI signals from the EEG input and graph representation, with graph pooling layers indexed by the number of electrodes.
- The PhysioNet dataset contains over 1,500 EEG records from 109 subjects, using 64 electrodes and four MI tasks: left fist, right fist, both fists, and both feet.
- The High Gamma dataset contributes four EEG tasks from 14 subjects using 44 electrodes, resampled at 250 Hz.
- Each time point is treated as a sample to represent instantaneous brain states rather than using time windows, supporting time-resolved EEG MI decoding.
- Experiments use 90% training data and 10% testing data, repeating the procedure 10 times with different random seeds to assess stability.
C. Graph Preliminary
The graph models EEG electrodes as nodes connected by weighted correlations. Absolute PCC values define the adjacency structure, which is then converted into degree and Laplacian matrices for graph processing.
- An EEG graph is defined by nodes, edges, and a weighted adjacency matrix encoding correlations between nodes.
- 1) Graph Representation:: The absolute PCC matrix captures correlation magnitude regardless of positive or negative sign, and adjacency is defined as A = |P| − I.
- 1) Graph Representation:: The degree matrix is diagonal, with each diagonal element obtained by summing the corresponding adjacency-row weights.
- 1) Graph Representation:: The combinatorial Laplacian is L = D − A, while the normalized Laplacian represents correlations between graph nodes through degree normalization.
- 1) Graph Representation:: The Laplacian is real, symmetric, and positive semidefinite, providing orthonormal graph Fourier modes for spectral processing.
2) Spectral Graph Filtering:
Spectral graph filtering transforms signals using the Laplacian’s eigenbasis, but direct filters are computationally expensive. Chebyshev polynomial approximations provide localized, efficient graph convolutional filtering.
- 2) Spectral Graph Filtering:: The graph Laplacian is decomposed into an eigenvector basis and eigenvalue matrix, enabling graph Fourier transformation of input signals.
- 2) Spectral Graph Filtering:: Graph convolution combines the graph-Fourier representation of a signal with a spectral filter before transforming the result back to the graph domain.
- 2) Spectral Graph Filtering:: Nonparametric spectral filters are not spatially localized and have high computational complexity, motivating polynomial filter approximations.
- 2) Spectral Graph Filtering:: The filter is parameterized as a truncated Chebyshev expansion using scaled Laplacian polynomials and Chebyshev coefficients.
- 2) Spectral Graph Filtering:: Chebyshev recursion avoids explicit graph Fourier-basis computation and reduces complexity from O(N^2) to O(KN).
3) Graph Coarsening and Fast Pooling:
Graph coarsening reduces graph dimensionality by repeatedly matching neighboring EEG nodes, forming coarser graphs, and pooling the reordered graph signal one-dimensionally.
- Graclus coarsening repeatedly matches unmarked neighboring nodes to construct progressively coarser graphs.The matching maximizes a local normalized-cut criterion, after which matched nodes are marked and their weights combined.
- At each level, matched node pairs are replaced by coarsened nodes whose weights equal the sum of the paired weights.
- The coarsest-level node ordering is propagated back to the finest level before one-dimensional graph-signal pooling.
- The algorithm halves the number of nodes between consecutive coarsening levels.
D. Model Initialization
The GCNs-Net initializes graph structure from absolute EEG-signal correlations and combines graph convolutions, pooling, nonlinear processing, and softmax prediction. Its design choices include empirically selected hyperparameters and polynomial-filter configurations evaluated across model structures.
- Model Initialization: The graph Laplacian is constructed from the absolute Pearson correlation matrix of overall EEG signals to represent electrode topology.The adjacency matrix is defined as A = |P| − I, where I is the identity matrix.
- Model Initialization: Graph convolutional layers learn generalized features, pooling layers reduce dimensionality, and a fully connected softmax layer produces the MI-task prediction.For 64 EEG channels, the architecture permits a maximum of six pooling layers.
- Model Initialization: The network applies batch normalization and Softplus activations in graph convolutional and fully connected layers.Softplus is used to prevent gradient vanishing, while batch normalization normalizes minibatch graph signals before scaling and shifting them.
- Model Initialization: The model uses cross-entropy loss with L2 regularization, with the weight-decay rate set to 1 × 10^-2.
E. Evaluation Metrics
The evaluation examines metrics, datasets, and architectural choices for GCNs-Net. Results show that deeper graph convolutions improve decoding, while second-order Chebyshev filters balance performance and model complexity.
- Evaluation Metrics: Accuracy, Kappa, precision, recall, F1-score, ROC, and AUC were used to evaluate decoding performance, with pair-wise t-tests at p=0.05 assessing significance.
- Dataset and Architecture Evaluation: The PhysioNet comparison used 20 subjects, 64 channels, and 1,075,200 samples to train and evaluate alternative architectures.
- Polynomial Order: Second-order Chebyshev filters were selected because polynomial orders above one had minor decoding differences while reducing model complexity relative to higher orders.
- Architecture Ablation: Increasing graph convolutional depth produced steep accuracy gains, whereas additional pooling layers yielded more modest improvements.
- Architecture Ablation: 88.60% accuracy was achieved by Model C6-P5-K2 and 88.85% by Model C6-P6-K2 at second-order polynomial approximation.
- Filters and Fully Connected Layers: More filters marginally increased accuracy but raised loss after an initial fall, indicating overfitting; extra fully connected layers gently reduced performance.
B. Subject-level Validation
Subject-level validation shows high but variable decoding accuracy across individuals and datasets. The High Gamma results support the model’s reported robustness to individual variability.
- PhysioNet Dataset: Subject accuracies on the PhysioNet Dataset ranged from 80.49% to 98.72% across the ten reported subjects.
- PhysioNet Dataset: Subject 10 achieved 98.72% accuracy, AUC 0.99, and class accuracies of 99.92%, 97.96%, 98.08%, and 98.93% for L, R, B, and F.
- High Gamma Dataset: 96.24% mean accuracy was achieved across 14 subjects on the High Gamma Dataset, with individual accuracies ranging from 90.43% to 99.18%.
C. Classification at the Group Level
Group-level evaluation reports strong performance across both benchmark datasets, including multi-class metrics on PhysioNet and accuracy and F1-score on High Gamma.
- PhysioNet Dataset: On 20 PhysioNet subjects, accuracy was 88.35%, Kappa 84.47%, precision 88.39%, recall 88.35%, and F1-score 88.34%.
- PhysioNet Dataset: PhysioNet class accuracies were 83.45%, 86.72%, 83.96%, and 99.42% for L, R, B, and F, respectively, with AUC 0.92.
- High Gamma Dataset: On the High Gamma Dataset, group-level accuracy was 80.89% and F1-score was 80.78% across 14 subjects.
D. 10-fold Cross-validation for Reliability
Repeated cross-validation produced stable group-level performance, while larger PhysioNet cohorts retained high testing accuracy. These results support reproducibility and scaling across subjects.
- Cross-validation Procedure: Ten-fold cross-validation divided the 20-subject PhysioNet dataset into ten parts, rotating one part as testing data and nine as training data.
- Reliability Results: 89.39% was the maximum accuracy and 87.90% the minimum across repetitive experiments, while averaged accuracy and F1-score were both 88.57%.
- Dataset Scaling: For 50 subjects, testing and training accuracies were 89.75% and 94.99%, respectively; for 100 subjects, they were 88.14% and 93.24%.
- Dataset Scaling: The larger-cohort results were reported to show that GCNs-Net learns generalized features from subjects at larger scale.
- Interpretation: The method was reported as effective and robust for graph-structured EEG motor-imagery signals because it considers the functional topological relationship of EEG electrodes.
F. Comparison with State-of-the-art
GCNs-Net is compared with existing EEG motor-imagery models at subject and group levels using maximum and averaged accuracy on PhysioNet and High Gamma datasets. It achieves competitive or dominant performance across these comparisons, including strong results for larger PhysioNet groups and High Gamma classification.
- PhysioNet Dataset: 89.39% maximum accuracy was achieved for 20 participants and 88.14% for 100 participants on the PhysioNet Dataset.These results are reported at the group level and are described as competitive with existing studies.
- PhysioNet Dataset: 30.21% maximum accuracy increment over the CNNs model was reported at the subject level, with a significant performance difference.The comparison is reported as statistically significant with p < 0.05.
- High Gamma Dataset: 99.18% maximum accuracy and 96.24% averaged accuracy were achieved by GCNs-Net on the High Gamma Dataset.The comparison with CNN-based methods was statistically significant, whereas the comparison with DAN was not significantly different.
- Cross-validation and robustness: 88.57% averaged accuracy was obtained after 10-fold cross-validation, indicating stable and reliable performance across repeated evaluation.The broader evaluation also reports convergence for personalized and group-wise predictions and robustness to individual variability.