This paper analyzes the kernel density estimation on spaces of Gaussian distributions endowed with different metrics. Expressions of kernels are provided for the 2-Wasserstein metric on the space of multivariate Gaussians. For the Fisher metric the kernels are provided only for univariate Gaussians and multivariate centered Gaussians. The density estimation is successfully applied to a classification problem of electro-encephalographic signals.

Brain Computer Interfaces (BCI) rely on brain waves signal, such as electro-encephalogram (EEG) recording, to endow a disabled user with non-muscular communication. Given the very low signal-to-noise ratio of EEG, a signal enhancement phase is crucial for ensuring decent performances in BCI systems. Several methods have been proposed for EEG signal enhancement, such as Independent Component Analysis, Common Spatial Pattern, and Principal Component Analysis. We show that Canonical Correlation Analysis (CCA), initially introduced to SSVEP-based BCI as a feature extraction method, is a good candidate for such preprocessing state. Evaluation is performed on a recording from 5 subjects during a BCI task based on Steady-State Visual Evoked Potentials (SSVEP). The authors demonstrate that CCA significantly improves classification performances in SSVEP-based BCIs.

Brain Computer Interfaces (BCI) based on electroencephalography (EEG) rely on multichannel brain signal processing. Most of the state-of-the-art approaches deal with covariance matrices, and indeed Riemannian geometry has provided a substantial framework for developing new algorithms. Most notably, a straightforward algorithm such as Minimum Distance to Mean yields competitive results when applied with a Riemannian distance. This applicative contribution aims at assessing the impact of several distances on real EEG dataset, as the invariances embedded in those distances have an influence on the classification accuracy. Euclidean and Riemannian distances and means are compared both in term of quality of results and of computational load.

In the context of assistive technologies, it is important to design systems that adapt to the user specificities, and to rely as much as possible on the residual capacities of each user. We define a new methodology in the context of assistive robotics: it is an hybrid approach where a physical interface is complemented by a Brain-Computer Interface (BCI). An implementation of such methodology is proposed, using a 3D touchless interface for continuous control and a steady-state visually evoked potential (SSVEP)-based BCI for triggering specific actions. We describe a novel algorithm for classification of SSVEP signals based on Canonical Correlation Analysis (CCA) and Support Vector Machines (SVM). Its reliability and robustness are assessed in an online setup and its results are compared to existing algorithms. Finally, an experimental evaluation of the proposed system is performed with a 3D navigation task in a Virtual Environment (VE). The system is also embedded on an assistive robotic arm exoskeleton to validate its feasibility.