Riemannian Weighting Enhances Multiclass Motor Imagery Brain Computer Interface Classification Accuracy

A research team has demonstrated an advanced feature extraction architecture that improves the classification of complex motor imagery signals in brain-computer interfaces by integrating Riemannian geometry-based weighting with filter bank common spatial patterns. Brain-computer interfaces were originally conceived to enable individuals with severe motor disabilities or paralysis to control assistive machinery, operate domestic appliances, and interact with computing software without requiring physical muscular exertion. Modern implementations extend into neurorehabilitation, cognitive enhancement, and prosthetic device management by translating electroencephalogram recordings collected from the human scalp into actionable operational commands. The primary operational bottleneck in motor imagery systems arises from the intricate, non-stationary, and noise-prone characteristics of raw brain waves, particularly when attempting to differentiate multiple distinct movement intentions simultaneously. To address these longstanding signal-processing hurdles, the investigators formulated the Riemannian-Weighting Filter Bank Common Spatial Pattern framework, which refines classical spatial filtering through non-Euclidean geometric principles to enhance multiclass discrimination.

Motor imagery paradigms operate by capturing distinct event-related desynchronization and event-related synchronization responses generated within the sensorimotor cortex when an individual mentally rehearses specific limb actions. While early brain-computer interface investigations concentrated on basic time-domain metrics such as mean, variance, skewness, and kurtosis to reduce computing overhead in embedded microprocessors, these scalar metrics proved inadequate for capturing subtle spatial and spectral brain dynamics across multiple classes. Subsequent frequency-based approaches monitored band power fluctuations within specific physiological bands, specifically the mu rhythm spanning 8 to 12 hertz and the beta rhythm spanning 13 to 30 hertz. Nevertheless, simple band power computations remain vulnerable to background noise and fail to exploit spatial relationships among distributed scalp recording channels. Although the standard Common Spatial Pattern method emerged as an effective tool for binary tasks by maximizing the signal variance of one class while minimizing that of another, traditional formulations rely on Euclidean arithmetic averaging of sample covariance matrices, rendering them fragile in the presence of artifacts, signal variability, and multiclass extensions.

The novel signal-processing architecture overcomes these structural constraints by operating directly within the Riemannian manifold of symmetric positive definite covariance matrices rather than treating matrices as flat Euclidean arrays. When covariance matrices are averaged via conventional arithmetic means, the underlying geometric curvature of the mathematical space is disregarded, which can severely distort class centroids when processing noisy trials or heterogeneous sample populations. The proposed pipeline computes trial-specific covariance matrices and evaluates pairwise geodesic distances using the matrix logarithm and Frobenius norm formulations. By determining intra-class Riemannian similarities, the method calculates weighted Riemannian Fréchet means through iterative tangent space projections. This adaptive weighting scheme systematically penalizes atypical outlier trials and noise spikes while assigning greater numerical influence to trials that reside near the geometric center of each motor imagery class distribution, establishing more stable and representative spatial filter foundations.

To transition the spatial filtering framework from standard two-class problems to a four-class classification environment, the researchers embedded a One-vs-Rest decomposition strategy directly into the Riemannian-weighted optimization process. Rather than pursuing a single unstable multiclass optimization function, the One-vs-Rest model separates the four-class challenge into four distinct binary sub-problems where each specific motor imagery action is evaluated against the aggregate pool of all remaining classes. For every binary sub-task, the complete Riemannian-weighting pipeline is executed independently, generating targeted spatial filters tailored to isolate the unique cortical topography of individual imagined movements. The architecture couples this spatial decomposition with a multiband filter bank decomposition that segregates continuous electroencephalogram signals into specific spectral sub-bands. This multiband decomposition improves local signal stationarity, enabling the model to extract class-specific spatial filters that capture narrow-band power variations that would otherwise be obscured in broader spectral windows.

The experimental validation of the proposed methodology was conducted using benchmark recordings from Data Set 2a of the BCI Competition IV, a standardized public repository comprising recordings from nine healthy human participants. The experimental protocol required subjects to mentally rehearse four discrete motor imagery tasks: imagined movement of the left hand, the right hand, both feet, and the tongue. Electroencephalogram signals were captured at a sampling frequency of 250 hertz using a twenty-two channel silver-and-silver-chloride electrode montage positioned according to the international 10–20 system, referenced to the left mastoid and grounded at the right mastoid, alongside three auxiliary electrooculographic recording channels. Prior to digitisation, the biosignal acquisition hardware applied an analog front-end bandpass filter spanning 0.5 to 100 hertz alongside a 50-hertz notch filter to reject powerline electrical interference. Each participant completed two distinct recording sessions separated across time, with each session comprising 288 trials distributed evenly across the four target motor tasks at 72 trials per class.

Before extracting Riemannian-weighted spatial features, the raw multichannel biosignals underwent a rigorous preprocessing sequence designed to suppress physiological artifacts and preserve cortical rhythms without introducing synthetic phase distortions. The three dedicated electrooculographic channels were proactively excluded from downstream feature extraction pipelines, physically isolating ocular artifacts caused by eye blinks and saccades without imposing heavy computational demands. The remaining twenty-two scalp channels were filtered using a zero-phase sixth-order Infinite Impulse Response Butterworth bandpass filter configured to isolate three physiologically relevant frequency bands: the mu rhythm from 8 to 13 hertz, the beta rhythm from 13 to 30 hertz, and the low gamma rhythm from 30 to 45 hertz. The researchers selected the sixth-order Butterworth design due to its maximally flat passband characteristics, which preserve precise amplitude and temporal phase relationships across sensorimotor oscillations while ensuring sharp roll-off attenuation against high-frequency electromyographic noise and low-frequency baseline drifts.

Following preprocessing, feature vectors were constructed by concatenating log-transformed band power values derived from each class-specific and sub-band-specific spatial filter, producing high-dimensional representations of combined spatial and spectral neural activation. To evaluate feature quality, the investigators trained and tested three separate machine learning classification algorithms: a linear model using Linear Discriminant Analysis, an ensemble structure using the Random Forest Classifier, and a non-linear Multi-Layer Perceptron neural network trained via error backpropagation. In addition to testing individual classifiers, the architecture incorporated a majority voting ensemble mechanism that combined the independent predictions generated by the three algorithms to establish a consensus classification decision for each trial, thereby mitigating individual model bias and enhancing overall decision stability across ambiguous signal boundaries.

Performance evaluation across the nine participants in the BCI Competition IV Dataset 2a demonstrated consistent classification gains across all evaluation metrics, encompassing classification accuracy, precision, recall, and F1-score calculated from true positive, true negative, false positive, and false negative counts. When paired with filter bank decomposition, the individual Linear Discriminant Analysis classifier reached an average accuracy of 80.40 percent, alongside an average recall of 80.40 percent, precision of 81.44 percent, and an F1-score of 80.47 percent. The Multi-Layer Perceptron model attained an average classification accuracy of 80.02 percent, while the Random Forest Classifier achieved an average accuracy of 80.90 percent. Implementing the majority voting ensemble across the three models yielded the highest overall performance on the four-class benchmark, securing 81.83 percent accuracy, 81.83 percent recall, 82.74 percent precision, and an F1-score of 81.87 percent.

Visualizations utilizing t-distributed stochastic neighbor embedding corroborated the numerical findings by illustrating marked differences in feature space clustering between standard Common Spatial Patterns, Riemannian filter bank patterns, and Riemannian-weighted filter bank patterns. Features generated by the proposed framework exhibited tighter, more segregated spatial clusters corresponding to the four motor imagery tasks, particularly for subjects exhibiting moderate initial separability. Significant inter-subject variability remained evident across the cohort, reflecting individual differences in electrode contact impedance, anatomical neuroanatomy, attention fluctuations, and cognitive engagement during recording sessions. For instance, in subject 2, who exhibited the lowest baseline performance, classification accuracy improved substantially from 55.90 percent under conventional processing to 70.49 percent under the Riemannian-weighted pipeline. At the opposite end of the performance spectrum, subject 8 achieved the highest individual results, demonstrating 93.06 percent accuracy and recall, 93.16 percent precision, and an F1-score of 93.08 percent under the proposed method.

Comparative benchmarking against previous signal-processing frameworks established the competitive position of the Riemannian-weighted approach relative to established literature baselines evaluated on the same public four-class dataset. Standard regularized spatial patterns combined with global filtering achieved lower average accuracies of 75.27 percent for Linear Discriminant Analysis, 73.73 percent for the neural network, and 74.35 percent for the random forest model. The proposed processing chain delivered approximately a 10 percent accuracy improvement over architectures that combine basic Common Spatial Patterns with Continuous Wavelet Transforms and Convolutional Neural Networks. Furthermore, the framework outperformed advanced spatial selection algorithms, including genetic-algorithm-tuned time-segment filter banks and adaptively filtered pattern models, by approximately 6 percent, highlighting the analytical benefit of incorporating Riemannian weighting directly into covariance matrix estimation rather than treating geometric transformations as isolated post-processing steps.

To evaluate broader generalization beyond the nine-subject four-class benchmark, the investigators adapted the processing pipeline to process two-class motor imagery recordings from the public Giga DB repository, which contains electroencephalogram recordings from 52 subjects. Across this larger cohort, the architecture maintained robust discrimination capabilities, yielding average classification accuracies of 90.06 percent with Linear Discriminant Analysis, 89.73 percent with the Random Forest Classifier, and 86.92 percent with the Multi-Layer Perceptron. Notably, individual subjects within the Giga DB cohort achieved peak performances, with subject S14 reaching 100 percent classification accuracy and subject S16 achieving 98.40 percent across the evaluated models. These results surpassed earlier literature benchmarks based on multistage combinations of multi-scale principal component analysis, variational mode decomposition, and cascade-forward neural networks, which achieved an average accuracy of approximately 85 percent on the same database.

Despite these measurable analytical improvements, the authors emphasized specific technical and experimental boundaries that govern the interpretation of their findings. All evaluations were conducted retrospectively on open-access benchmark databases recorded in controlled laboratory settings, meaning that the complete processing chain has not yet undergone prospective clinical validation on newly recorded, real-time patient streams. The computational implementation relied on offline epoch splitting and randomized cross-validation protocols rather than closed-loop neuroprosthetic control experiments. To facilitate independent verification and algorithmic benchmarking, the research group deposited the complete signal-processing source code, preprocessed trial matrices, and analysis scripts in publicly accessible open-science repositories. Looking ahead, the researchers proposed investigating the integration of advanced multivariate variational mode decomposition into the Riemannian spatial filtering pipeline to further enhance signal stability, reduce calibration time, and support practical clinical translation for motor-impaired individuals.

Subject of Research: Multiclass motor imagery brain-computer interface signal processing using Riemannian geometry and filter bank common spatial patterns

Article Title: Filter bank CSP with Riemannian weighting for disability-centric motor imagery brain computer interface

Article References: Jihen, S., Karmani, S., Belwafi, K., Jemmali, M., & Djemal, R. (2026). Filter bank CSP with Riemannian weighting for disability-centric motor imagery brain computer interface. Brain Informatics, 13(1), Article 12. https://doi.org/10.1186/s40708-026-00295-0

Image Credits: AI Generated

DOI: 10.1186/s40708-026-00295-0

Keywords: Brain-computer interfaces, Electroencephalogram, Motor imagery, Common Spatial Pattern, Riemannian geometry, Filter bank, Linear Discriminant Analysis, Random Forest Classifier, Multilayer Perceptron, BCI Competition IV dataset 2a, Covariance matrices, One-vs-Rest decomposition, Signal preprocessing, Sensorimotor rhythms, Giga DB dataset, Majority voting ensemble, Symmetric positive definite matrices