International audienceClassical dictionary learning algorithms (DLA) allow unicomponent signals to be processed. Due to our interest in two-dimensional (2D) motion signals, we wanted to mix the two components to provide rotation invariance. So, multicomponent frameworks are examined here. In contrast to the well-known multichannel framework, a multivariate framework is first introduced as a tool to easily solve our problem and to preserve the data structure. Within this multivariate framework, we then present sparse coding methods: multivariate orthogonal matching pursuit (M-OMP), which provides sparse approximation for multivariate signals, and multivariate DLA (M-DLA), which empirically learns the characteristic patterns (or features) that are associated to a multivariate signals set, and combines shift-invariance and online learning. Once the multivariate dictionary is learned, any signal of this considered set can be approximated sparsely. This multivariate framework is introduced to simply present the 2D rotation invariant (2DRI) case. By studying 2D motions that are acquired in bivariate real signals, we want the decompositions to be independent of the orientation of the movement execution in the 2D space. The methods are thus specified for the 2DRI case to be robust to any rotation: 2DRI-OMP and 2DRI-DLA. Shift and rotation invariant cases induce a compact learned dictionary and provide robust decomposition. As validation, our methods are applied to 2D handwritten data to extract the elementary features of this signals set, and to provide rotation invariant decomposition

International audienceChallenges for the next generation of Brain Computer Interfaces (BCI) are to mitigate the common sources of variability (electronic, electrical, biological) and to develop online and adaptive systems following the evolution of the subject's brain waves. Studying electroencephalographic (EEG) signals from their associated covariance matrices allows the construction of a representation which is invariant to extrinsic perturbations. As covariance matrices should be estimated, this paper first presents a thorough study of all estimators conducted on real EEG recording. Working in Euclidean space with covariance matrices is known to be error-prone, one might take advantage of algorithmic advances in Riemannian geometry and matrix manifold to implement methods for Symmetric Positive-Definite (SPD) matrices. Nonetheless, existing classification algorithms in Riemannian spaces are designed for offline analysis. We propose a novel algorithm for online and asynchronous processing of brain signals, borrowing principles from semi-unsupervised approaches and following a dynamic stopping scheme to provide a prediction as soon as possible. The assessment is conducted on real EEG recording: this is the first study on Steady-State Visually Evoked Potential (SSVEP) experimentations to exploit online classification based on Rie-mannian geometry. The proposed online algorithm is evaluated and compared with state-of-the-art SSVEP methods, which are based on Canonical Correlation Analysis (CCA). It is shown to improve both the classification accuracy and the information transfer rate in the online and asynchronous setup