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

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.

Cross-subject motor imagery decoding remains a fundamental challenge in EEG-based brain-computer interfaces due to substantial inter-subject variability. Recent approaches have leveraged Riemannian geometry by representing EEG signals as covariance matrices on the symmetric positive definite (SPD) manifold. However, existing methods primarily focus on manifold-based representations while largely overlooking subject-specific variations in covariance dispersion and orientation. In this work, we address these challenges through geometry-aware congruence transformations and propose three complementary models: (i) Discriminative Congruence Transform (DCT), (ii) Deep Linear DCT (DLDCT), and (iii) Deep DCT-UNet (DDCT-UNet). The proposed models are evaluated both as manifold alignment modules for downstream classifiers and as end-to-end discriminative architectures optimized via cross-entropy with a custom logistic regression head. Experiments on challenging cross-subject motor imagery benchmarks demonstrate consistent improvements in transductive decoding performance, achieving 2-3% higher accuracy than strong baselines. These results highlight the effectiveness of geometry-aware congruence learning for mitigating inter-subject variability in EEG decoding.

Electroencephalography (EEG) has become one of the key modalities underpinning brain-computer interfaces (BCIs) due to its high temporal resolution, rapid responsiveness, non-invasiveness, low cost, and portability. However, EEG signals are substantially inferior to intracranial EEG (iEEG) in signal-to-noise ratio and local spatial resolution, whereas iEEG suffers from extremely limited clinical accessibility owing to its invasive nature, hindering widespread application. To address this challenge, this study proposes a unified data-and prior knowledge-driven framework for EEG-iEEG representational enhancement. Guided by the principle that "geometric structure dictates function", the framework maps static cortical anatomy onto dynamic constraints governing neural signal propagation and integrates general-purpose neural representations extracted by a pre-trained large EEG model to explicitly model signal transmission through the brain. Enhanced EEG signals are then synthesized via a multidimensional representation diffusion process. Numerous experimental results demonstrate that the generated enhanced EEG signals effectively recover the neural activity patterns lost during propagation through the brain. This finding indicates that the performance ceiling of BCIs is constrained not only by acquisition hardware but also by the depth to which the generative model resolves the mechanisms of neural signal propagation. Collectively, the proposed framework provides a viable pathway toward acquiring high-fidelity neural signals at low cost.