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Transferring Subspaces Between Subjects in Brain-Computer Interfacing
Wojciech Samek, Frank C. Meinecke, Klaus-Robert Müller
TL;DR
Session-to-session changes make reliable BCI classification difficult, while common multi-subject methods may rely on discriminative similarity that varies across users. The paper transfers shared non-stationarity patterns from other subjects to construct invariant features, and experiments show improved performance with physiologically meaningful change patterns.
Problem
BCI must handle changing signal distributions between training and testing, while discriminative subspaces can differ substantially across subjects.
Method
The method estimates common non-stationary directions from other subjects and regularizes CSP filters toward their orthogonal complement without transferring discriminative information.
Results
The experiments show performance gains from transferring non-stationarity information, with dominant experimental-condition changes more stable across subjects than discriminative subspaces.
Takeaways & Limitations
Non-discriminant noise can define invariant features, and transferred non-stationarity patterns can have a physiologically interpretable meaning.
Abstract
from arXiv · showhide
Compensating changes between a subjects' training and testing session in Brain Computer Interfacing (BCI) is challenging but of great importance for a robust BCI operation. We show that such changes are very similar between subjects, thus can be reliably estimated using data from other users and utilized to construct an invariant feature space. This novel approach to learning from other subjects aims to reduce the adverse effects of common non-stationarities, but does not transfer discriminative information. This is an important conceptual difference to standard multi-subject methods that e.g. improve the covariance matrix estimation by shrinking it towards the average of other users or construct a global feature space. These methods do not reduces the shift between training and test data and may produce poor results when subjects have very different signal characteristics. In this paper we compare our approach to two state-of-the-art multi-subject methods on toy data and two data sets of EEG recordings from subjects performing motor imagery. We show that it can not only achieve a significant increase in performance, but also that the extracted change patterns allow for a neurophysiologically meaningful interpretation.
I. INTRODUCTION
BCI transfer methods commonly use other subjects to reduce calibration demands, but inter-subject variability and EEG non-stationarity make shared discriminative representations unreliable. This paper instead transfers common non-stationarity information to construct invariant features.
- Motivation: EEG non-stationarity and large inter-subject variation can make shared representations or classifiers deteriorate performance.The authors emphasize that careful subject selection or weighting is essential when using other subjects.
- Core approach: The proposed method transfers non-stationarity information rather than task-relevant discriminative information from other subjects.It aims to reduce training-test shift without assuming similar discriminative subspaces.
- Assumptions: The method assumes principal non-stationarities are similar across subjects and that removing them benefits classification.Its spatial filters are regularized away from the common non-stationary subspace rather than toward another subject’s discriminative subspace.
- Use case: Transfer is especially useful when experimental conditions differ between calibration and testing sessions.A visual cue present only during testing can create increased occipital activity that produces non-stationary features.
- Scope: Discriminative-subspace regularization and non-stationarity transfer are complementary approaches with different assumptions and application scenarios.The former is most promising with scarce data and high subject similarity, whereas the latter targets common experimental non-stationarities.
II. RELATED WORK
Related BCI work seeks robust features under changing signal distributions, often by adapting CSP or incorporating other subjects. Existing multi-subject methods generally assume similarity in covariance structure or spatial filters rather than directly reducing session-to-session shift.
- Problem setting: Covariate shift in BCI arises because measured brain signals change between training and testing phases.Robust-representation methods address this by extracting features less affected by underlying brain-process variation.
- CSP background: CSP discriminates motor-imagery states by maximizing band-power variance in one condition while minimizing it in the other.Because CSP can overfit and does not ensure feature stationarity, multiple variants have been proposed.
- Covariance-based transfer: Covariance regularization incorporates other subjects’ data to improve high-dimensional covariance estimation when data are scarce.Its regularization parameter controls how much information is incorporated from other users.
- Covariance-based transfer: Covariance-based transfer assumes similar covariance matrices across subjects, an assumption often violated by large inter-subject variability.Sequential subject selection was proposed to address this issue.
- Spatial-filter transfer: Another CSP variant decomposes each subject’s filter into global and subject-specific components under a shared optimization framework.This approach assumes similarity between spatial filters extracted from different subjects.
III. TRANSFERRING NON-STATIONARITIES
The paper’s stationary-subspace CSP transfers common non-stationary directions learned from other subjects and removes them before CSP feature computation. It estimates prominent training-test changes, compresses them into a shared subspace, and regularizes filters toward its orthogonal complement.
- Overview: The method transfers non-stationary information between subjects to bridge the gap between training and test data.It is presented as a multi-subject approach specifically targeting non-stationarity.
- Change extraction: For each other subject, prominent change directions are extracted from an eigendecomposition of the training-test covariance difference.Eigenvectors with the largest absolute eigenvalues capture the dominant changes.
- Subspace construction: Aggregated change directions form a common non-stationary subspace whose dimensionality is reduced with PCA.The resulting subspace basis is represented by the columns of P, and its dimension can otherwise grow with the data matrix size.
- Stationary Subspace CSP: The algorithm computes the non-stationary subspace from other subjects to achieve invariant features for the target user.Table I summarizes this cross-subject construction.
- Stationary Subspace CSP: CSP filters are regularized toward the orthogonal complement of the common non-stationary subspace by adding a penalty matrix to the CSP denominator.The penalty matrix is formed from the reduced-rank projection matrix, with λ set high to remove non-stationary directions.
- Parameters: The approach requires parameters controlling extracted change directions and the dimensionality of the removed non-stationary subspace.These parameters may be fixed or selected adaptively, but cannot be determined by cross-validation on the target subject for the stated goal.
B. General Considerations
Transfer between subjects can target discriminative information, non-stationary changes, or both, with each strategy depending on different cross-subject similarities. Selecting among these approaches is difficult when similarity is hard to estimate, and transferred information must be carefully regularized.
- Discriminative and non-stationary information support different transfer-learning scenarios: the former helps with scarce data, whereas the latter helps address common experimental-related changes.
- When neither discriminative nor non-stationary subspaces are shared, transfer learning is not applicable and CSP is the method of choice.
- If discriminative or non-stationary directions are shared, corresponding multi-subject methods may outperform CSP; combining methods is favored when both types are transferable.
- Method selection requires estimating subject or subspace similarity, which may be impossible without test data and may require many other subjects for reliable selection or clustering.
- Regularization parameters control transferred information, and poor choices may reduce performance when subject similarity is low; ssCSP additionally limits transfer by the removed non-stationary subspace size.
- A motivating example has varying discriminative subspaces but common, relatively small non-stationary subspaces, making non-stationarity transfer more promising.
A. Toy Experiment
The toy experiments vary the similarity of discriminative and non-stationary subspaces separately and together to test when transferred information remains useful. ssCSP is robust to dissimilar discriminative subspaces and loses little when transferred non-stationary information becomes meaningless.
- Data generation: The toy data mixes stationary task-relevant and irrelevant sources with non-stationary noise through random rotation matrices, using low-dimensional discriminative and non-stationary subspaces.The discriminative subspace contains six sources, while the non-stationary component contains five sources whose variance changes between training and test data.
- Discriminative-subspace dissimilarity: Increasing dissimilarity between subjects’ discriminative subspaces makes covCSP and mtCSP increasingly ineffective, whereas ssCSP remains unaffected and improves classification when non-stationarities are shared.The transferred discriminative information becomes meaningless as mixing matrices diverge, but ssCSP does not transfer discriminative information.
- Non-stationary-subspace dissimilarity: With fixed discriminative subspaces and increasingly different non-stationary directions, covCSP and mtCSP remain stable, while ssCSP improves when transferred information is meaningful and returns approximately to CSP-level performance otherwise.The limited performance loss reflects regularizing away from a small subspace, which removes fewer potentially important directions.
- Combined dissimilarity: When both subspaces differ, multi-subject methods provide no advantage over CSP and discriminative-information transfer can reduce performance; when both are shared, all methods improve significantly.The best results in the shared-subspace case come from ssCSP and the ss+mtCSP combination.
B. Data Set
The study uses two EEG motor-imagery datasets and compares standard CSP with three multi-subject approaches, including covariance, multitask, and non-stationarity transfer methods.
- Data sets: Two calibration recordings from five healthy participants involve left-hand and foot motor imagery, with visual or auditory task cues.Each training and test set contains 132 trials, equally distributed across classes.
- Preprocessing: Both datasets use 8–30 Hz filtering and extract cue-triggered motor-imagery segments before analysis.The first dataset uses 750–3500 ms segments, while the second uses 500–2500 ms segments.
- Data sets: A second dataset contains EEG recordings from five healthy subjects performing right-hand and foot motor imagery without feedback.It uses two visual cue types and provides 280 trials per subject.
- Methods: The comparison includes standard CSP, covCSP regularized with other subjects’ covariance matrices, mtCSP, and ssCSP for non-stationarity transfer.covCSP and mtCSP are evaluated across specified trade-off parameters, with mtCSP initialized from CSP filters.
C. Initial Analysis
The initial analysis compares covariance and subspace similarities across subjects and between training and test sessions. It finds that discriminative subspaces differ more across subjects than dominant non-stationary directions.
- Covariance similarity: Cross-subject covariance differences are up to two orders of magnitude larger than within-subject training–test differences.Distances are measured with symmetric Kullback–Leibler divergence between covariance matrices.
- Subspace similarity: Subspace similarity is measured as the mean squared cosine of principal angles, corresponding to projected energy preserved between subspaces.Higher values indicate closer subspaces, and considering all principal angles gives a fuller comparison.
- Subspace construction: Discriminative subspaces are built from CSP filters with the largest eigenvalues, whereas non-stationary subspaces use directions with the largest absolute training–test eigenvalue changes.These definitions distinguish task-discriminative structure from session-related changes.
- Cross-subject comparison: Canonical-correlation comparisons show that discriminant subspaces are quite different between subjects, unlike dominant non-stationary directions.The figure represents pairwise comparisons with individual markers and mean similarities as solid lines.
D. Performance Comparison
The performance comparison shows that multi-subject information can improve results, but benefits vary by subject and method focus. Combining non-stationarity removal with multitask CSP produces the best reported performance, with improvements over CSP significant up to 95%.
- Real-data results: Multi-subject data improve performance overall, but individual subjects benefit unequally from the compared methods.The reported beneficiaries differ across methods, including A4, B1, B3, A1, and B5.
- Method focus: covCSP and mtCSP target estimation, whereas ssCSP targets non-stationarity rather than covariance estimation.The different objectives explain why their performance benefits are not uniform across users.
- Combined approach: The combined method first projects out the ssCSP non-stationary subspace, then computes mtCSP spatial filters using its original-data regularization parameters.This combination gives the best performance results among the evaluated approaches.
- Statistical testing: The improvement over the CSP baseline is significant up to 95% according to paired permutation tests with 210 permutations.The tests estimate empirical mean-performance-difference distributions by swapping method performances across subject permutations.
E. Interpretation
The transferred non-stationary directions correspond to interpretable changes between visual and auditory stimulation, while ssCSP largely removes training–test feature-distribution shifts compared with CSP.
- Interpretation: The five most non-stationary directions are highly similar between users and focus on occipital and temporal activity linked to visual and auditory processing.These patterns reflect the transition from visual to auditory stimulus presentation.
- Interpretation: Visualizing subject A3’s directions shows that the principal non-stationary patterns capture the change from visual to auditory stimulus presentation.The cited directions involve occipital and temporal areas.
- Interpretation: Fig. 6 shows a significant training–test feature-distribution change for CSP, whereas the change becomes almost negligible with ssCSP.The comparison uses the two most discriminative dimensions for subject A1.
- Interpretation: Table III compares classification accuracies across multi-subject CSP variants, with the best overall performance reported for the combination of ssCSP and MTCSP.All subjects except B2 profit from information transfer.
- Interpretation: Table V reports mean classification accuracies for the session-to-session transfer experiment.The table summarizes training on the first session and testing on later sessions.
F. Reducing Between-Day Variability
The method is applied to variability across recording days, where transfer learning improves performance only slightly because between-day non-stationarities are less similar across subjects.
- F. Reducing Between-Day Variability: The experiment evaluates transfer learning for non-stationarities arising when training and test recordings occur on different days.Reducing this variability is described as crucial for zero-training BCI systems.
- F. Reducing Between-Day Variability: The data comprise five subjects performing left- and right-hand motor imagery across five calibration sessions, with 140–288 trials per session.Visual stimuli indicated the task before each 3–3.5-second imagery period.
- F. Reducing Between-Day Variability: Performance increased when applying transfer learning, but the effect was rather small because prominent between-day non-stationarities were less similar across subjects.This variability is therefore less stable across subjects than changes induced by differing experimental conditions.
G. Learning from Noise ?
The paper finds that prominent shifts lie mainly outside discriminative CSP directions, yet this non-discriminative subspace can still help construct invariant features and improve BCI classification.
- G. Learning from Noise ?: CSP and non-stationary subspaces have similarities below the lower 1% quantile of random-subspace comparisons, indicating that most shift lies in non-discriminative data.Similarity is measured using mean square cosine of principal angles.
- G. Learning from Noise ?: Removing discriminative CSP directions before estimating non-stationarity yields average performance 78.1 versus 78.9 for the original ssCSP method.The performance loss is minimal and not significant.
- G. Learning from Noise ?: The non-discriminative noise subspace can aid invariant-feature construction, challenging the view that noise never helps classification or adaptation.The subspace is generally removed by CSP before classification.
- G. Learning from Noise ?: The discussion concludes that transferred non-stationarity information is mainly in the non-discriminant noise part and can define invariant features.The extracted patterns are described as physiologically interpretable and meaningful.