Florian Yger

sw-SVM: sensor weighting support vector machines for EEG-based brain?computer interfaces

In many machine learning applications, like brain-computer interfaces (BCI), high-dimensional sensor array data are available. Sensor measurements are often highly correlated and signal-to-noise ratio is not homogeneously spread across sensors. Thus, collected data are highly variable and discrimination tasks are challenging. In this work, we focus on sensor weighting as an efficient tool to improve the classification procedure. We present an approach integrating sensor weighting in the classification framework. Sensor weights are considered as hyper-parameters to be learned by a support vector machine (SVM). The resulting sensor weighting SVM (sw-SVM) is designed to satisfy a margin criterion, that is, the generalization error. Experimental studies on two data sets are presented, a P300 data set and an error-related potential (ErrP) data set. For the P300 data set (BCI competition III), for which a large number of trials is available, the sw-SVM proves to perform equivalently with respect to the ensemble SVM strategy that won the competition. For the ErrP data set, for which a small number of trials are available, the sw-SVM shows superior performances as compared to three state-of-the art approaches. Results suggest that the sw-SVM promises to be useful in event-related potentials classification, even with a small number of training trials.

Riemannian Approaches in Brain-Computer Interfaces: A Review

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.

Learning with infinitely many features

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).

Averaging covariance matrices for EEG signal classification based on the CSP: An empirical study

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.

Importance-weighted covariance estimation for robust common spatial pattern

New estimator for covariance matrices based on the importance-weighting of samples.Embedded in CSP algorithm it makes CSP more robust to non-stationarity.We show the complementarity of a robust feature extraction and a robust classifier.Using an importance-weighted classifier, we improve the robustness of the whole BCI. Non-stationarity is an important issue for practical applications of machine learning methods. This issue particularly affects Brain-Computer Interfaces (BCI) and tends to make their use difficult. In this paper, we show a practical way to make Common Spatial Pattern (CSP), a classical feature extraction that is particularly useful in BCI, robust to non-stationarity. To do so, we did not modify the CSP method itself, but rather make the covariance estimation (used as input by every CSP variant) more robust to non-stationarity. Those robust estimators are derived using a classical importance-weighting scenario. Finally, we highlight the behavior of our robust framework on a toy dataset and show gains of accuracy on a real-life BCI dataset.

Geometry-aware principal component analysis for symmetric positive definite matrices

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.

Oblique principal subspace tracking on manifold

This paper addresses the problem of principal subspace tracking in presence of a colored noise. We propose to extend the YAST algorithm to handle such a case. We also propose a Riemannian framework that could benefit to other classical trackers. Finally, as a proof of concept, our method is compared to the only oblique tracker of the literature on a toy dataset.

A Vascular Endothelial Growth Factor-Dependent Sprouting Angiogenesis Assay Based on an In Vitro Human Blood Vessel Model for the Study of Anti-Angiogenic Drugs

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.

Large marginwavelet-based dictionary for signal classification

This paper addresses the problem of automatic wavelet feature extraction for signal classication. We propose to jointly learn wavelet-based features (including scale and translation of the wavelet as well as its shape) and a decision function by casting the problem as a Multi-Kernel Learning problem. A novel active constraints algorithm is then proposed. Our method has been tested on a toy dataset and compared to classical methods with competitive results.