Riemannian Geometry-Preserving Variational Autoencoder for MI-BCI Data Augmentation

Viktorija Poļaka; Ivo Pascal de Jong; Andreea Ioana Sburlea

cs.LGMar 11, 2026

Riemannian Geometry-Preserving Variational Autoencoder for MI-BCI Data Augmentation

Authors: Viktorija Poļaka, Ivo Pascal de Jong, Andreea Ioana Sburlea

Organizations: Faculty of Science and Engineering, University of Groningen, Groningen, The Netherlands

Abstract

This paper addresses the challenge of generating synthetic electroencephalogram (EEG) covariance matrices for motor imagery brain-computer interface (MI-BCI) applications. Objective: We aim to develop a generative model capable of producing high-fidelity synthetic covariance matrices while preserving their symmetric positive-definite nature. Approach: We propose a Riemannian geometry-preserving variational autoencoder (RGP-VAE) integrating geometric mappings with a composite loss function combining Riemannian distance, tangent space reconstruction accuracy and generative diversity. Results: The model generates valid, representative EEG covariance matrices, while learning a subject-invariant latent space. Synthetic data proves practically useful for MI-BCI, with its impact depending on the paired classifier. Contribution: This work introduces and validates the RGP-VAE as a geometry-preserving generative model for EEG covariance matrices, highlighting its potential for signal privacy, scalability and data augmentation.

Figures & tables

Figure 1: An overview of the proposed RGP-VAE, illustrating the integration of a standard VAE with geometric operations on the SPD manifold. An input SPD matrix $\mathbf{X}_{i}$ is first projected onto the tangent space at a reference point $\mathbf{P}_{\text{ref}}$ using the logarithmic map $\text{log}_{\mathbf{P}_{\text{ref}}}$ (Eq. 3 ). This tangent representation $\mathbf{S}_{i}$ is then vectorized to serve as the encoder input $\mathbf{H}_{\text{tangent}}$ . The encoder maps this input to a latent distribution parameterized by $\boldsymbol{\mu}$ and $\text{log}(\boldsymbol{\sigma}^{2})$ , from which a latent vector $\mathbf{z}_{i}$ is sampled and passed to the decoder to produce the reconstructed vector $\mathbf{H}_{\text{decoded}}$ . The vector is unvectorized back into a tangent space representation $\hat{\mathbf{S}}_{i}$ , which is finally mapped back onto the SPD manifold via the exponential map ( $\text{exp}_{\mathbf{P}_{\text{ref}}}$ ) (Eq. 4 ) to produce the reconstructed SPD matrix $\hat{\mathbf{X}}_{i}$ .

Figure 2: 2D UMAP visualization of the latent space of the RGP-VAE for right-hand movement data. Points are colored by Subject ID; their significant overlap indicates the learning of a subject-invariant representation.

Figure 3: Distribution of accuracy improvement for each classifier using the prior generator. The plot shows the percentage point difference between the ‘Augmented’ and ‘Synthetic-Only’ conditions relative to the ‘Baseline’ across all subjects. The red line signifies the mean whilst the blue line is the median.

Figure 4: Distribution of accuracy improvement for each classifier using the posterior generator, showing similar trends to the prior generator but with more pronounced fluctuations.

Generator	Statistical Variance		Geometric Diversity
	Original	Synthetic (Ratio)	Original	Synthetic
Prior	0.208	0.221 (1.061)	2.032	1.946
Posterior	0.208	0.221 (1.063)	2.032	1.918

Table 1: Fidelity analysis of synthetic data averaged across 12 folds. The table compares the statistical variance ratio and the mean intra-class Riemannian distance, showing that the synthetic data distribution is valid.

Generator	Classifier	Baseline	Augmented Scenario			Synthetic-Only Scenario
Generator	Classifier	Acc. (%)	Acc. (%)	Improvement	p-value	Acc. (%)	Improvement	p-value
Prior	MDM	$59.52\pm 5.52$	$58.92\pm 5.40$	-0.59%	0.092	$58.36\pm 5.03$	-1.16%	0.043
	KNN	$53.19\pm 4.00$	$55.38\pm 4.17$	+2.19%	0.003	$56.19\pm 4.19$	+3.00%	$\mathbf{<0.001}$
	SVC	$60.67\pm 5.33$	$57.43\pm 6.32$	-3.24%	0.016	$56.75\pm 6.37$	-3.92%	0.002
Posterior	MDM	$59.52\pm 5.52$	$58.83\pm 5.29$	-0.69%	0.092	$58.95\pm 5.51$	-0.57%	0.151
	KNN	$53.19\pm 4.00$	$55.64\pm 4.13$	+2.45%	0.002	$56.68\pm 4.06$	+3.49%	0.002

Table 2: Average balanced accuracy (

\%

) across 12 subjects for all training conditions and generators with corresponding p-values.

Synthetic Data Augmentation

Synthetic data augmentation creates or modifies training examples to improve learning when real data are scarce, imbalanced, costly, or sensitive.

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Jul 22, 2026J/K move · Enter open · S save

Generative Augmentation for EEG Motor Imagery Classification: A Class-Conditional VAE with Cycle-Consistent Decoder Refinement

Matei Moldoveanu, Alain Sirois, Claire Ben Ali, Fabien Lotte+1

Naqi Logix, Paris, France · Inria Center at Univ. Bordeaux / LaBRI, Talence, France · LITIS, INSA Rouen-Normandy, France

Synthetic Data Augmentation MI Classification Conditional Variational Autoencoder EEG Signal Generation

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We investigate whether a generative model can supply useful synthetic motor-imagery (MI) electroencephalography (EEG) trials that improve the accuracy of independent downstream classifiers. We train a class-conditional variational autoencoder (CVAE) with an integrated latent classifier on the Zhou motor-imagery dataset, using the learned per-class prior as a generator: sampling the prior for a given label and decoding it into a synthetic, label-consistent signal. A constraint on the covariance matrix of the generated data encourages preservation of covariance structure, and the model is trained with a schedule that alternates ordinary VAE training with a decoder-focused phase that sharpens the generative pathway used for augmentation. We measure the effect of adding synthetic trials to the training set under two evaluation protocols -- within-user (pooled 60/20/20 split across subjects) and cross-user (leave-one-subject-out, LOSO) -- across four representative EEG classification pipelines: Common Spatial Patterns with Linear Discriminant Analysis (CSP+LDA), tangent-space features with a Support Vector Machine (TGSP+SVM), Minimum Distance to Riemannian Mean (MDM), and a neural network based on EEGNetv4 (henceforth EEGNet). Results are aggregated across independent augmentation draws, random seeds (within-user), or leave-one-subject-out folds (cross-user), with uncertainty reported as 95% confidence intervals (Student's

t

-distribution) computed over per-seed/per-fold averages. We find that synthetic EEG from the CVAE is most credible as a source of class-structured, covariance-like data rather than as a substitute for real raw EEG: it can raise the point estimate for MDM, but the broader augmentation claim remains conservative -- observed gains are small and classifier-dependent.

Abstract

Synthetic Data Augmentation

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