Riemannian tangent space mapping and elastic net regularization for cost-effective EEG markers of brain atrophy in Alzheimer's disease

The diagnosis of Alzheimer's disease (AD) in routine clinical practice is most commonly based on subjective clinical interpretations. Quantitative electroencephalography (QEEG) measures have been shown to reflect neurodegenerative processes in AD and might qualify as affordable and thereby widely available markers to facilitate the objectivization of AD assessment. Here, we present a novel framework combining Riemannian tangent space mapping and elastic net regression for the development of brain atrophy markers. While most AD QEEG studies are based on small sample sizes and psychological test scores as outcome measures, here we train and test our models using data of one of the largest prospective EEG AD trials ever conducted, including MRI biomarkers of brain atrophy.Comment: Presented at NIPS 2017 Workshop on Machine Learning for Healt

EEG-Based User Reaction Time Estimation Using Riemannian Geometry Features

Riemannian geometry has been successfully used in many brain-computer interface (BCI) classification problems and demonstrated superior performance. In this paper, for the first time, it is applied to BCI regression problems, an important category of BCI applications. More specifically, we propose a new feature extraction approach for Electroencephalogram (EEG) based BCI regression problems: a spatial filter is first used to increase the signal quality of the EEG trials and also to reduce the dimensionality of the covariance matrices, and then Riemannian tangent space features are extracted. We validate the performance of the proposed approach in reaction time estimation from EEG signals measured in a large-scale sustained-attention psychomotor vigilance task, and show that compared with the traditional powerband features, the tangent space features can reduce the root mean square estimation error by 4.30-8.30%, and increase the estimation correlation coefficient by 6.59-11.13%.Comment: arXiv admin note: text overlap with arXiv:1702.0291

Fixed point algorithms for estimating power means of positive definite matrices

Estimating means of data points lying on the Riemannian manifold of symmetric positive-definite (SPD) matrices has proved of great utility in applications requiring interpolation, extrapolation, smoothing, signal detection, and classification. The power means of SPD matrices with exponent p in the interval [-1, 1] interpolate in between the Harmonic mean (p = -1) and the Arithmetic mean (p = 1), while the Geometric (Cartan/Karcher) mean, which is the one currently employed in most applications, corresponds to their limit evaluated at 0. In this paper, we treat the problem of estimating power means along the continuum p ϵ (-1, 1) given noisy observed measurement. We provide a general fixed point algorithm (MPM) and we show that its convergence rate for p = ±0.5 deteriorates very little with the number and dimension of points given as input. Along the whole continuum, MPM is also robust with respect to the dispersion of the points on the manifold (noise), much more than the gradient descent algorithm usually employed to estimate the geometric mean. Thus, MPM is an efficient algorithm for the whole family of power means, including the geometric mean, which by MPM can be approximated with a desired precision by interpolating two solutions obtained with a small ±p value. We also present an approximated version of the MPM algorithm with very low computational complexity for the special case p = ±½. Finally, we show the appeal of power means through the classification of brain-computer interface event-related potentials data

Riemannian channel selection for BCI with between-session non-stationarity reduction capabilities

L'institution a financé les frais de publication pour que cet article soit en libre accèsInternational audienceObjective: Between-session non-stationarity is a major challenge of current Brain-Computer Interfaces (BCIs) that affects system performance. In this paper, we investigate the use of channel selection for reducing between-session non-stationarity with Riemannian BCI classifiers. We use the Riemannian geometry framework of covariance matrices due to its robustness and promising performances. Current Riemannian channel selection methods do not consider between-session non-stationarity and are usually tested on a single session. Here, we propose a new channel selection approach that specifically considers non-stationarity effects and is assessed on multi-session BCI data sets. Methods: We remove the least significant channels using a sequential floating backward selection search strategy. Our contributions include: 1) quantifying the non-stationarity effects on brain activity in multi-class problems by different criteria in a Riemannian framework and 2) a method to predict whether BCI performance can improve using channel selection. Results: We evaluate the proposed approaches on three multi-session and multi-class mental tasks (MT)-based BCI datasets. They could lead to significant improvements in performance as compared to using all channels for datasets affected by between-session non-stationarity and to significant superiority to the state-of-the-art Riemannian channel selection methods over all datasets, notably when selecting small channel set sizes. Conclusion: Reducing non-stationarity by channel selection could significantly improve Riemannian BCI classification accuracy. Significance: Our proposed channel selection approach contributes to make Riemannian BCI classifiers more robust to between-session non-stationarities

Classification Approaches in Neuroscience: A Geometrical Point of View

Functional magnetic resonance images (fMRI) are brain scan images by MRI machine which are taken functionally cross the time. Several studies have investigated methods analyzing such images (or actually the drawn data from them) and is interestingly growing up. For examples models can predict the behaviours and actions of people based on their brain pattern, which can be useful in many fields. We do the classification study and prediction of fMRI data and we develop some approaches and some modifications on them which have not been used in such classification problems. The proposed approaches were assessed by comparing the classification error rates in a real fMRI data study. In addition, many programming codes for reading from fMRI scans and codes for using classification approaches are provided to manipulate fMRI data in practice. The codes, can be gathered later as a package in R. Also, there is a steadily growing interest in analyzing functional data which can often exploit Riemannian geometry. As a prototypical example of these kind of data, we will consider the functional data rising from an electroencephalography (EEG) signal in Brain-Computer interface (BCI) which translates the brain signals to the commands in the machine. It can be used for people with physical inability and movement problems or even in video games, which has had increased interest. To do that, a classification study on EEG signals has been proposed, while, the data in hand to be classified are matrices. A multiplicative algorithm (MPM), which is a fast and efficient algorithm, was developed to compute the power means for matrices which is the crucial step in our proposed approaches for classification. In addition, some simulation studies were used to examine the performance of MPM against existing algorithms. We will compare the behavior of different power means in terms of accuracy in our classifications, which had not been discovered previously. We will show that it is hard to have a guess to find the optimal power mean to have higher accuracy depending on the multivariate distribution of data available. Then, we also develop an approach, combination of power means, to have the benefit of all to improve the classification performance. All the codes related to the fast MPM algorithms and the codes for manipulating EEG signals in classification are written in MATLAB and can be developed later as a package

Online SSVEP-based BCI using Riemannian geometry

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