This paper provides a comprehensive overview of the modern classification algorithms used in EEG-based BCIs, presents the principles of these methods and guidelines on when and how to use them. It also identifies a number of challenges to further advance EEG classification in BCI.

Although promising from numerous applications, current brain-computer interfaces (BCIs) still suffer from a number of limitations. In particular, they are sensitive to noise, outliers and the non-stationarity of electroencephalographic (EEG) signals, they require long calibration times and are not reliable. Thus, new approaches and tools, notably at the EEG signal processing and classification level, are necessary to address these limitations. Riemannian approaches, spearheaded by the use of covariance matrices, are such a very promising tool slowly adopted by a growing number of researchers. This article, after a quick introduction to Riemannian geometry and a presentation of the BCI-relevant manifolds, reviews how these approaches have been used for EEG-based BCI, in particular for feature representation and learning, classifier design and calibration time reduction. Finally, relevant challenges and promising research directions for EEG signal classification in BCIs are identified, such as feature tracking on manifold or multi-task learning.

Angiogenesis is the formation of new capillaries from pre-existing blood vessels and participates in proper vasculature development. In pathological conditions such as cancer, abnormal angiogenesis takes place. Angiogenesis is primarily carried out by endothelial cells, the innermost layer of blood vessels. The vascular endothelial growth factor-A (VEGF-A) and its receptor-2 (VEGFR-2) trigger most of the mechanisms activating and regulating angiogenesis, and have been the targets for the development of drugs. However, most experimental assays assessing angiogenesis rely on animal models. We report an in vitro model using a microvessel-on-a-chip. It mimics an effective endothelial sprouting angiogenesis event triggered from an initial microvessel using a single angiogenic factor, VEGF-A. The angiogenic sprouting in this model is depends on the Notch signaling, as observed in vivo. This model enables the study of anti-angiogenic drugs which target a specific factor/receptor pathway, as demonstrated by the use of the clinically approved sorafenib and sunitinib for targeting the VEGF-A/VEGFR-2 pathway. Furthermore, this model allows testing simultaneously angiogenesis and permeability. It demonstrates that sorafenib impairs the endothelial barrier function, while sunitinib does not. Such in vitro human model provides a significant complimentary approach to animal models for the development of effective therapies.

Symmetric positive definite (SPD) matrices in the form of covariance matrices, for example, are ubiquitous in machine learning applications. However, because their size grows quadratically with respect to the number of variables, high-dimensionality can pose a difficulty when working with them. So, it may be advantageous to apply to them dimensionality reduction techniques. Principal component analysis (PCA) is a canonical tool for dimensionality reduction, which for vector data maximizes the preserved variance. Yet, the commonly used, naive extensions of PCA to matrices result in sub-optimal variance retention. Moreover, when applied to SPD matrices, they ignore the geometric structure of the space of SPD matrices, further degrading the performance. In this paper we develop a new Riemannian geometry based formulation of PCA for SPD matrices that (1) preserves more data variance by appropriately extending PCA to matrix data, and (2) extends the standard definition from the Euclidean to the Riemannian geometries. We experimentally demonstrate the usefulness of our approach as pre-processing for EEG signals and for texture image classification.

We propose a principled framework for learning with infinitely many features, situations that are usually induced by continuously parametrized feature extraction methods. Such cases occur for instance when considering Gabor-based features in computer vision problems or when dealing with Fourier features for kernel approximations. We cast the problem as the one of finding a finite subset of features that minimizes a regularized empirical risk. After having analyzed the optimality conditions of such a problem, we propose a simple algorithm which has the flavour of a column-generation technique. We also show that using Fourier-based features, it is possible to perform approximate infinite kernel learning. Our experimental results on several datasets show the benefits of the proposed approach in several situations including texture classification and large-scale kernelized problems (involving about 100 thousand examples).

This paper presents an empirical comparison of covariance matrix averaging methods for EEG signal classification. Indeed, averaging EEG signal covariance matrices is a key step in designing brain-computer interfaces (BCI) based on the popular common spatial pattern (CSP) algorithm. BCI paradigms are typically structured into trials and we argue that this structure should be taken into account. Moreover, the non-Euclidean structure of covariance matrices should be taken into consideration as well. We review several approaches from the literature for averaging covariance matrices in CSP and compare them empirically on three publicly available datasets. Our results show that using Riemannian geometry for averaging covariance matrices improves performances for small dimensional problems, but also the limits of this approach when the dimensionality increases.

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The omnipresence of non-stationarity and noise in Electroencephalogram signals restricts the ubiquitous use of Brain-Computer interface. One of the possible ways to tackle this problem is to adapt the computational model used to detect and classify different mental states. Adapting the model will possibly help us to track the changes and thus reducing the effect of non-stationarities. In this paper, we present different adaptation strategies for state of the art Riemannian geometry based classifiers. The offline evaluation of our proposed methods on two different datasets showed a statistically significant improvement over baseline non-adaptive classifiers. Moreover, we also demonstrate that combining different (hybrid) adaptation strategies generally increased the performance over individual adaptation schemes. Also, the improvement in average classification accuracy for a 3-class mental imagery BCI with hybrid adaption is as high as around 17% above the baseline non-adaptive classifier.