Cross-Subject and Cross-Montage EEG Transfer Learning via Individual Tangent Space Alignment and Spatial-Riemannian Feature Fusion

The gist: Individual Tangent Space Alignment (ITSA), a novel pre-alignment strategy, enhances cross-subject generalisation in EEG transfer learning by incorporating subject-specific recentering, distribution matching, and supervised rotational alignment to fuse Regularised Common Spatial Patterns with Riemannian geometry.

Introduction and Motivation

Personalised music-based interventions offer a powerful means of supporting motor rehabilitation by dynamically tailoring auditory stimuli to provide external timekeeping cues, modulate affective states, and stabilise gait patterns The integration of musical stimulus with rehabilitative EEG-based BCI for gait rehabilitation presents a novel approach to bridge between motor recovery, emotional regulation and user engagement A considerable challenge in EEG-based BCIs is crosssubject generalisation, where models trained on one population must perform on entirely unseen individuals Variability results from anatomical differences, electrode position shifts between sessions and inter-subject variations in brain functions Additionally, auditory gait rehabilitation involves subjects in motion, which introduces movement artifacts and muscle activity that compromise EEG signal quality.

Proposed Methodology: Individual Tangent Space Alignment (ITSA)

The proposed pre-alignment strategy incorporates three key innovations to mitigate inter-subject variability in leave-one-subject-out (LOSO) classification scenarios 1) subjectspecific recentering that individually aligns each subject’s covariance matrices, which ensures that all subjects share a common global mean, M - the identity matrix 2) distribution matching through feature rescaling, where both the training and testing datasets are rescaled to match their distribution around their respective centres of mass 3) supervised rotational alignment with robust calibration procedures, which involves deriving transformation parameters from a calibration subset and applying them to the evaluation subset.

Feature Extraction and Fusion Architecture

The work builds on previous works [20] to introduce a hybrid feature extraction architecture that fuses Regularised Common Spatial Patterns (RCSP) with Riemannian geometry techniques in both sequential and parallel configurations 1) Regularisation of Covariance Matrices: covariance matrices are regularised using Diagonal Loading, where C˜k is the regularised counterpart of the spatial covariance matrix, Ck for class, k The regularization is performed by shrinking each covariance matrix towards the identity matrix shown in Equation 12. 2) Integration Approaches: Fusion is explored in two approaches: ‘Sequential RCSP-Rie’ and ‘Parallel RCSP-Rie’ a) Sequential Integration (“Sequential (Seq.) RCSPRiemannian Features”) combines the two techniques sequentially - firstly spatially filtering signals, followed by TS projection and (half) vectorisation to obtain input features b) Parallel Integration (“Parallel (Par.) RCSPRiemannian Feature”) combines these two techniques in a parallel approach, where both spatially filtered features and tangent space features are obtained simultaneously and horizontally concatenated to obtain input features.

Evaluation and Results

The evaluation framework employs rigorous leave-onesubject-out cross-validation with statistical validation The results demonstrate superior performance with ‘ITSA’ and parallel RCSPRiemannian fusion. 1) Performance Improvements by Condition: In the advanced tempo condition, the proposed pre-alignment strategy enhanced performance for 10 subjects (subjects 1, 4, 6, 7, 10, 11, 12, 16, and 17 and subject-specific recentering that individually aligns each subject’s covariance matrices In the delayed tempo condition, the ‘Par. RCSP-Rie’ method demonstrated more robust improvements. 2) Statistical Analysis and Significance Testing: Statistical analysis confirmed significant improvements across all tested configurations, with the Advance Tempo condition showing significant improvement (t(17) = 2.3256, p = 0.03267).

Cross-Montage Validation

To simulate montage-specific testing datasets, channel-specific subsets were extracted from the original high-density 108-electrodes dataset, mimicking 10-10 and 10-20 montage configurations The results demonstrate the potential of cross-montage experimentation, yielding promising outcomes. For both Seq. and Par. RCSP-Rie approaches and temporal conditions, applying ‘ITSA’ across all three montages (108 electrodes, 10-10 and 10-20) consistently outperformed their respective baseline counterparts when ‘ITSA’ was not implemented.

Conclusion

The proposed pre-alignment strategy - ‘Individual Tangent Space Alignment’ (ITSA), integrated with a fusion of Common Spatial Patterns and Riemannian geometry to improve the model’s generalisability in a leave-one-subject-out cross-validation (LOSOCV) The substantial performance degradation observed without pre-alignment highlights the negative impact of inter-subject variability on model generalisation Our proposed method demonstrated consistent statistical improvements across all feature extraction methods and temporal conditions. Crucially, our cross-montage experiments demonstrated the practical advantage of the ITSA-RCSP-Riemannian fusion framework. The ability to train on high-density electrode arrays while maintaining performance on clinical-grade montages significantly enhances practical deployment feasibility. Generalisable BCIs can therefore support personalised musical interventions, where the musical stimuli are dynamically tailored to provide external timekeeping cues while modulating affective state, stabilising gait patterns and enhancing user’s ability to initiate and adapt gait parameters.

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Cross-Subject and Cross-Montage EEG Transfer Learning via Individual Tangent Space Alignment and Spatial-Riemannian Feature Fusion Nicole Lai-Tan, Xiao Gu, Marios G. Philliastides, Fani Deligianni Abstract—Personalised music-based interventions offer a powerful means of supporting motor rehabilitation by dynamically tailoring auditory stimuli to provide external timekeeping cues, modulate affective states, and stabilise gait patterns Generalisable Brain-Computer Interfaces (BCIs) thus hold promise for adapting these interventions across individuals However, inter-subject variability in EEG signals, further compounded by movement-induced artefacts and motor planning differences, hinders the generalisability of BCIs and results in lengthy calibration processes. We propose Individual Tangent Space Alignment (ITSA), a novel pre-alignment strategy incorporating subject-specific recentering, distribution matching, and supervised rotational alignment to enhance cross-subject generalisation Our hybrid architecture fuses Regularised Common Spatial Patterns (RCSP) with Riemannian geometry in parallel and sequential configurations, improving class separability while maintaining the geometric structure of covariance matrices for robust statistical computation Using leave-one-subject-out cross-validation, ‘ITSA’ demonstrates significant performance improvements across subjects and conditions The parallel fusion approach shows the greatest enhancement over its sequential counterpart, with robust performance maintained across varying data conditions and electrode configurations The code will be made publicly available at the time of publication. Index Terms—EEG-based BCIs, Music-based gait rehabilitation, Sensorimotor Entrainment, Rhythmic cueing, Crosssubject variability, Transfer learning, Pre-alignment strategies, Regularised common spatial patterns, Riemannian Geometry

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domain scenarios with different channel configurations Furthermore the integration of spatial filtering techniques with geometric alignment methods remains underexplored Common Spatial Patterns (CSP) excel at maximising class separability [18] while Riemannian geometry-based methods preserve the statistical structure of covariance matrices [19] As such, fusion of CSP and Riemannian approaches could enable greater interpretability via spatial projections that reveal how discriminative features relate to neurophysiological processes, while also preserving the underlying covariant structure captured by Riemannian geometry

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1. Proper implementation of Individual Tangent Space Alignment (ITSA) for cross-subject transfer learning enables mitigating inter-subject variability by incorporating subject-specific recentering, distribution matching through feature rescaling, and supervised rotational alignment. This allows the AI system to generalize its learned features effectively to unseen individuals without lengthy calibration processes.

2. Fusion of Regularised Common Spatial Patterns (RCSP) with Riemannian geometry, implemented in both 'Sequential RCSP-Rie' and 'Parallel RCSP-Rie' configurations, improves class separability by enhancing discriminative features while simultaneously preserving the geometric structure of covariance matrices for more accurate statistical computations. This results in more robust statistical computations compared to using either method alone.

3. The ability to simulate testing datasets from high-density EEG data (108 electrodes) onto lower-density configurations (10-10 and 10-20 montages) while maintaining performance demonstrates the potential of cross-montage experimentation. This allows the improved AI system to be deployed in more practical, portable EEG setups with reduced complexity and computational demand.

4. The proposed framework can improve BCI systems generalisability by demonstrating that the use of ‘ITSA’ improves models’ generalisability to unseen subjects even in lower-density configurations. This means the system trained on one population can perform better on entirely different, unseen individuals or setups.

Personalised music-based interventions offer a powerful means of supporting motor rehabilitation by dynamically tailoring auditory stimuli to provide external timekeeping cues, modulate affective states, and stabilise gait patterns. Generalisable Brain-Computer Interfaces (BCIs) thus hold promise for adapting these interventions across individuals. However, inter-subject variability in EEG signals, further compounded by movement-induced artefacts and motor planning differences, hinders the generalisability of BCIs and results in lengthy calibration processes. We propose Individual Tangent Space Alignment (ITSA), a novel pre-alignment strategy incorporating subject-specific recentering, distribution matching, and supervised rotational alignment to enhance cross-subject generalisation. Our hybrid architecture fuses Regularised Common Spatial Patterns (RCSP) with Riemannian geometry in parallel and sequential configurations, improving class separability while maintaining the geometric structure of covariance matrices for robust statistical computation. Using leave-one-subject-out cross-validation, `ITSA' demonstrates significant performance improvements across subjects and conditions. The parallel fusion approach shows the greatest enhancement over its sequential counterpart, with robust performance maintained across varying data conditions and electrode configurations. The code will be made publicly available at the time of publication.