The non-stationary nature of electroencephalography (EEG) introduces distribution shifts across domains (e.g., days and subjects), posing a significant challenge to EEG-based neurotechnology generalization. Without labeled calibration data for target domains, the problem is a source-free unsupervised domain adaptation (SFUDA) problem. For scenarios with constant label distribution, Riemannian geometry-aware statistical alignment frameworks on the symmetric positive definite (SPD) manifold are considered state-of-the-art. However, many practical scenarios, including EEG-based sleep staging, exhibit label shifts. Here, we propose a geometric deep learning framework for SFUDA problems under specific distribution shifts, including label shifts. We introduce a novel, realistic generative model and show that prior Riemannian statistical alignment methods on the SPD manifold can compensate for specific marginal and conditional distribution shifts but hurt generalization under label shifts. As a remedy, we propose a parameter-efficient manifold optimization strategy termed SPDIM. SPDIM uses the information maximization principle to learn a single SPD-manifold-constrained parameter per target domain. In simulations, we demonstrate that SPDIM can compensate for the shifts under our generative model. Moreover, using public EEG-based brain-computer interface and sleep staging datasets, we show that SPDIM outperforms prior approaches.

Electroencephalography (EEG) based brain-computer interfaces (BCIs) face great challenges in generalizing across different domains (i.e., sessions and subjects) without costly supervised calibration.To avoid supervised calibration, transfer learning, particularly unsupervised domain adaptation, has been a popular approach.In this work, we focus on a geometric deep learning framework previously proposed for EEG-based mental imagery BCIs.The framework aligns marginal feature distributions in latent space, assuming identical label distributions across domains.Here, we propose a novel approach integrating data augmentation and clustering techniques to align the latent distributions under label shifts.

In human neuroimaging, multi-modal imaging techniques are frequently combined to enhance our comprehension of whole-brain dynamics and improve diagnosis in clinical practice. Modalities like electroencephalography and functional magnetic resonance imaging provide distinct views to the brain dynamics due to diametral spatiotemporal sensitivities and underlying neurophysiological coupling mechanisms. These distinct views pose a considerable challenge to learning a shared representation space, especially when dealing with covariance-based data characterized by their geometric structure. To capitalize on the geometric structure, we introduce a measure called geodesic correlation which expands traditional correlation consistency to covariance-based data on the symmetric positive definite (SPD) manifold. This measure is derived from classical canonical correlation analysis and serves to evaluate the consistency of latent representations obtained from paired views. For multi-view, self-supervised learning where one or both latent views are SPD we propose an innovative geometric deep learning framework termed DeepGeoCCA. Its primary objective is to enhance the geodesic correlation of unlabeled, paired data, thereby generating novel representations while retaining the geometric structures. In simulations and experiments with multi-view and multi-modal human neuroimaging data, we find that DeepGeoCCA learns latent representations with high geodesic correlation for unseen data while retaining relevant information for downstream tasks.

Symmetric positive definite (SPD) matrices, and in particular co-variance matrices as data descriptors find widespread application in various fields but also pure machine learning. SPD matrices form a Riemannian manifold, demanding machine learning methods that take this structure into account. In this work, we extend upon previous works and propose a batch normalization algorithm for the SPD manifold that can be readily combined with SPD neural networks and unlike previous works controls both the Fréchet mean and variance on the SPD manifold. The proposed method is validated in simulations and datasets with small sample sizes from three application domains: action recognition from human motion trajectories, image classification and mental imagery detection of electroencephalographic (EEG) signals. The combined results show a systematic performance increase upon previous works and tangent space approximations, as well as improved robustness to low signal-to-noise ratios and lack of data as often encountered in neuroimaging and brain-computer interfacing (BCI).

Electroencephalography (EEG) provides access to neuronal dynamics non-invasively with millisecond resolution, rendering it a viable method in neuroscience and healthcare. However, its utility is limited as current EEG technology does not generalize well across domains (i.e., sessions and subjects) without expensive supervised re-calibration. Contemporary methods cast this transfer learning (TL) problem as a multi-source/-target unsupervised domain adaptation (UDA) problem and address it with deep learning or shallow, Riemannian geometry aware alignment methods. Both directions have, so far, failed to consistently close the performance gap to state-of-the-art domain-specific methods based on tangent space mapping (TSM) on the symmetric, positive definite (SPD) manifold.Here, we propose a machine learning framework that enables, for the first time, learning domain-invariant TSM models in an end-to-end fashion. To achieve this, we propose a new building block for geometric deep learning, which we denote SPD domain-specific momentum batch normalization (SPDDSMBN). A SPDDSMBN layer can transform domain-specific SPD inputs into domain-invariant SPD outputs, and can be readily applied to multi-source/-target and online UDA scenarios. In extensive experiments with 6 diverse EEG brain-computer interface (BCI) datasets, we obtain state-of-the-art performance in inter-session and -subject TL with a simple, intrinsically interpretable network architecture, which we denote TSMNet. Code: https://github.com/rkobler/TSMNet

Naive users often perceive calibration of a Sensory Motor Rhythm (SMR) based Brain-Computer Interfaces (BCI) as tedious and lengthy. The lack of feedback during training is assumed to be a major cause. I.e. if one had already a reasonable model to start with, feedback training could be started immediately. One concept to address this issue is learning a general model and adapting it to new observations. In this study we applied this concept by utilizing a generative model entitled Restricted Boltzmann Machine (RBM). We investigated its feature extraction capabilities by fitting a RBM to recordings of 9 subjects. Generalization was assessed in an online co-adaptive study, covering 12 volunteers (10 naïve). An overall median accuracy of 88.9% (83.5% naïve) with a standard-error of 6.5% (6.6% naïve) was achieved for a classical hand versus feet motor imagery task. The online co-adaptive training itself lasted approximately 25 minutes. Feedback was already presented after a one minute setup run, whose purpose was to estimate initial statistics and to train an online artifact detection system.