Source-linked AI summary
Transfer Learning for Brain-Computer Interfaces: A Euclidean Space Data Alignment Approach
He He, Dongrui Wu
TL;DR
Subject differences make EEG transfer learning difficult, especially when new-subject data are scarce or unlabeled. The paper aligns EEG trials directly in Euclidean space, enabling flexible downstream algorithms at lower computational cost. Offline and simulated online MI and ERP experiments verified EA’s effectiveness and efficiency against RA and non-alignment approaches.
Problem
Individual differences complicate transfer learning for EEG-based BCIs, motivating methods that improve performance for new subjects with minimal or no subject-specific data.
Method
EA aligns EEG trials directly in Euclidean space using a subject-specific arithmetic covariance reference, without requiring labeled new-subject trials.
Results
Offline and simulated online experiments on two MI datasets and one ERP dataset verified EA’s effectiveness and efficiency.
Takeaways & Limitations
EA supports broad signal-processing, feature-extraction, and machine-learning choices while avoiding labeled new-subject data.
Takeaways & Limitations
RA-MDRM for ERP classification requires labeled non-target and target trials from the new subject, so it cannot operate without new-subject labels.
Abstract
from arXiv · showhide
Objective: This paper targets a major challenge in developing practical EEG-based brain-computer interfaces (BCIs): how to cope with individual differences so that better learning performance can be obtained for a new subject, with minimum or even no subject-specific data? Methods: We propose a novel approach to align EEG trials from different subjects in the Euclidean space to make them more similar, and hence improve the learning performance for a new subject. Our approach has three desirable properties: 1) it aligns the EEG trials directly in the Euclidean space, and any signal processing, feature extraction and machine learning algorithms can then be applied to the aligned trials; 2) its computational cost is very low; and, 3) it is unsupervised and does not need any label information from the new subject. Results: Both offline and simulated online experiments on motor imagery classification and event-related potential classification verified that our proposed approach outperformed a state-of-the-art Riemannian space data alignment approach, and several approaches without data alignment. Conclusion: The proposed Euclidean space EEG data alignment approach can greatly facilitate transfer learning in BCIs. Significance: Our proposed approach is effective, efficient, and easy to implement. It could be an essential pre-processing step for EEG-based BCIs.
I. INTRODUCTION
EEG-based BCIs use motor imagery and event-related potentials, but subject differences complicate transfer learning. The paper proposes Euclidean-space alignment to make trials more comparable while retaining flexible downstream processing.
- EEG is the most popular BCI input, with motor imagery and event-related potentials serving as the paper’s two classification scenarios.
- Transfer learning uses labeled data from source subjects to improve performance in a target subject, but inter-subject discrepancies can hinder this transfer.
- Riemannian alignment improves MDRM performance in motor imagery and ERP tasks but requires labeled subject-specific calibration trials for ERP classification.
- Euclidean alignment transforms EEG trials directly, allowing subsequent signal processing, feature extraction, and machine learning with broad algorithmic compatibility.
- The approach is computationally faster than Riemannian alignment and uses only unlabeled trials from the new subject.
- Effectiveness is evaluated in offline unsupervised and simulated online supervised classification scenarios.
A. Riemannian Distance
Riemannian distance measures separation between symmetric positive definite matrices on their manifold. Its geometry includes congruence invariance, while the Riemannian mean generally requires iterative computation.
- The Riemannian distance between SPD matrices is the geodesic, defined as the minimum curve length connecting them on the Riemannian manifold.
- The distance is computed from the Frobenius norm and the real eigenvalues of P_1^-1P_2.
- Riemannian distance remains unchanged under an invertible linear transformation, a property called congruence invariance.
- An SPD-matrix mean can be computed arithmetically in Euclidean space or geometrically as a Riemannian mean.
- The Riemannian mean minimizes the sum of squared Riemannian distances and has no closed-form solution, so it is usually computed iteratively.
C. MDRM
MDRM classifies trials by their covariance matrices and classwise Riemannian means, while RA-MDRM aligns covariance matrices using a resting-state reference. ERP requires trial augmentation to preserve temporal information.
- MDRM assigns a trial to the class whose Riemannian mean is closest to its covariance matrix.
- RA-MDRM computes a Riemannian mean from resting-trial covariance matrices and uses it as the reference for alignment.
- The alignment centers reference states at the identity matrix and reduces cross-session or cross-subject differences when the reference is appropriately estimated.
- In rapid serial visual presentation ERP, non-target stimuli serve as resting-state trials, making some labeled new-subject trials necessary.
- For motor imagery, a trial covariance matrix encodes discriminative spatial brain-activity information.
- ERP covariance matrices are augmented by concatenating the mean ERP trial with each trial so covariance captures temporal and spatial information.
E. Limitations of RA
RA is limited by covariance-level alignment, expensive Riemannian-mean computation, and labeled-data requirements for ERP transfer. EA addresses these constraints by aligning trials in Euclidean space using an arithmetic reference.
- RA-MDRM aligns covariance matrices rather than EEG trials, restricting subsequent classifiers to those operating directly on covariance matrices.
- Computing the Riemannian mean is time-consuming, especially when the number of EEG channels is large.
- ERP RA-MDRM requires labeled new-subject trials, preventing use when the new subject provides no label information.
- EA is designed to require no labeled new-subject data and to be computed more efficiently than RA.
- EA estimates an arithmetic mean covariance reference for each subject before performing alignment.
- After EA, each subject’s mean covariance matrix equals the identity matrix, making covariance distributions more similar across subjects.
- From an MMD perspective, EA seeks smaller distances between subject distributions because smaller distances indicate greater distributional similarity.
B. Comparison with RA
EA and RA both preserve Riemannian distances among covariance matrices, but EA aligns EEG trials directly in Euclidean space using an arithmetic-mean reference, making it broader and faster than RA.
- Both EA and RA preserve the Riemannian distances among covariance matrices after alignment.
- EA uses the Euclidean arithmetic mean of all covariance matrices, whereas RA uses the Riemannian mean of resting-state covariance matrices.
- EA aligns time-domain EEG trials directly, while RA aligns covariance matrices in the Riemannian space.
- EA supports subsequent signal processing, feature extraction, and machine learning methods, giving it broader applications than RA.
- EA can be computed much faster than RA because it uses an arithmetic rather than a Riemannian mean.
- EA and CORAL both reduce domain differences without target labels, but EA operates on 2D EEG trials and aligns mean covariance matrices across domains.
IV. DATASETS
The study uses two motor-imagery datasets and one ERP dataset, then visualizes how EA changes EEG trials and reduces differences between test and training subjects.
- The experiments use two motor-imagery datasets and one ERP dataset.
- Dataset 1 contains seven healthy subjects, 59-channel EEG, two selected imagery classes, and 100 trials per class during calibration.
- Dataset 2a contains nine healthy subjects performing four imagery tasks with 22-channel EEG and 3-channel EOG recorded at 250Hz.
- Both motor-imagery datasets were band-pass filtered, with trials extracted from 0.5 to 3.5 seconds after cue onset and resting states from 4.25 to 5.25 seconds.
- The ERP dataset contains rapid image presentations from 11 healthy subjects, classified into target and non-target images.
- After EA, EEG magnitudes become smaller and more uniform, while t-SNE shows training and test trials overlapping as their discrepancies decrease.
V. PERFORMANCE EVALUATION: OFFLINE UNSUPERVISED CLASSIFICATION
Offline unsupervised evaluation compares Euclidean and Riemannian alignment with unaligned baselines across two motor-imagery datasets. EA-CSP-LDA generally improves classification while substantially reducing computation time.
- Leave-one-subject-out cross-validation treats one subject as the test set and the remaining subjects as labeled training data.
- The compared methods are MDRM, RA-MDRM, CSP-LDA, and EA-CSP-LDA, with the latter aligning trials before CSP filtering and LDA classification.
- EA-CSP-LDA outperformed CSP-LDA on 14 of 16 subjects and RA-MDRM on 11 of 16 subjects, while RA-MDRM outperformed MDRM on 15 of 16.
- EA reduced classification accuracy for a small number of subjects, including Subjects 4 and 9 in Dataset 2a.
- EA-CSP-LDA significantly outperformed CSP-LDA on both datasets, significantly exceeded RA-MDRM on Dataset 1, and performed comparably to RA-MDRM on Dataset 2a.
- EA-CSP-LDA was 3.6-19.5 times faster than RA-MDRM and had a much smaller standard deviation in computing time.
- Overall, EA was more effective and efficient than RA in offline unsupervised motor-imagery classification.
C. Offline Classification Results on the ERP Dataset
Offline unsupervised ERP classification evaluated Euclidean alignment against non-aligned baselines because the Riemannian approach requires labeled new-subject trials. EA improved both SVM pipelines and achieved statistically significant gains.
- RA-MDRM was excluded because ERP alignment requires non-target trials and MDRM requires target trials from the new subject.
- The comparison included SVM, EA-SVM, xDAWN-SVM, and EA-xDAWN-SVM, with EA applied before PCA-based classification.
- EA-SVM outperformed SVM on 9 of 11 subjects, while EA-xDAWN-SVM outperformed xDAWN-SVM on 8 of 11 subjects.
- EA-xDAWN-SVM slightly outperformed EA-SVM on average, suggesting alignment may help xDAWN realize more of its potential.
- Paired t-tests found EA-SVM significantly outperformed SVM and EA-xDAWN-SVM significantly outperformed xDAWN-SVM.
D. Discussion: Different Choices of the Reference Matrix
Reference-matrix choice affected alignment performance. Imagery-trial references generally outperformed resting-trial references, with Euclidean and Riemannian means favoring their corresponding classifiers.
- RA uses resting covariance matrices, whereas EA estimates its reference matrix from all trials for both MI and ERP classification.
- MI reference matrices vary by trial type and mean geometry: resting or imagery trials can use either Riemannian or Euclidean means.
- Across both MI datasets, imagery-based references outperformed resting-based references for both MDRM and CSP-LDA.
- EI was best for CSP-LDA, RI was best for MDRM, and EI-CSP-LDA outperformed RI-MDRM across all 16 subjects on average.
VI. PERFORMANCE EVALUATION: SIMULATED ONLINE SUPERVISED CLASSIFICATION
Simulated online supervised classification assessed performance as labeled trials from a new subject arrived sequentially. Euclidean alignment generally improved MI transfer and often surpassed Riemannian alignment.
- Online learning began with no new-subject trials and added labeled trials sequentially to train classifiers with auxiliary-subject data.
- The simulation used a small online pool and evaluated future trials while incrementally adding new-subject samples to training.
- Reference matrices for EA and RA used the available new-subject trials, without requiring labels for alignment.
- RA-MDRM outperformed MDRM on 15 of 16 subjects, while EA-CSP-LDA outperformed CSP-LDA on 14 of 16 subjects.
- EA-CSP-LDA outperformed RA-MDRM on 12 of 16 subjects, and online comparisons used mean AUC over labeled-trial counts from 4 to 40.
C. Simulated Online Classification Results on the ERP Dataset
Online ERP classification compared aligned and non-aligned pipelines as labeled trials accumulated. Euclidean alignment improved both classifier families and significantly outperformed the alternatives in testing.
- MDRM and RA-MDRM were available online because labeled new-subject trials supported construction of augmented ERP trials.
- The experiment used 80 online trials, added 10 per iteration, started with 20 trials, and repeated each subject 30 times.
- On average, RA-MDRM outperformed MDRM and EA-xDAWN-SVM outperformed xDAWN-SVM.
- EA-xDAWN-SVM outperformed RA-MDRM on all 11 subjects.
- Paired t-tests showed EA-xDAWN-SVM significantly outperformed all three other approaches.
VII. CONCLUSION AND FUTURE RESEARCH
EA directly aligns EEG trials in Euclidean space, addressing limitations of Riemannian alignment while supporting broader algorithms, faster computation, and unlabeled new-subject data. Its benefits were verified across offline and simulated online classification, but current evaluations and shift correction remain limited.
- EA aligns EEG trials directly in Euclidean space, allowing signal processing, feature extraction, and machine learning algorithms to operate on the aligned trials.
- EA can be computed several times faster than Riemannian alignment and does not require labeled trials from the new subject.
- Offline and simulated online experiments on two motor-imagery datasets and one ERP dataset verified EA’s effectiveness and efficiency.
- EA considers covariate shift but ignores prior probability and concept shifts, so per-class distributions may remain discrepant across subjects.
- EA may increase concept shift or be affected by bad trials and outliers, helping explain improved performance on most but not all subjects.
- Simulated online experiments are not identical to real online experiments, motivating validation in real-world closed-loop BCI experiments.