Almost all EEG-based brain-computer interfaces (BCIs) need some labeled subject-specific data to calibrate a new subject, as neural responses are different across subjects to even the same stimulus. So, a major challenge in developing high-performance and user-friendly BCIs is to cope with such individual differences so that the calibration can be reduced or even completely eliminated. This paper focuses on the latter. More specifically, we consider an offline application scenario, in which we have unlabeled EEG trials from a new subject, and would like to accurately label them by leveraging auxiliary labeled EEG trials from other subjects in the same task. To accommodate the individual differences, we propose a novel unsupervised approach to align the EEG trials from different subjects in the Euclidean space to make them more consistent. It has three desirable properties: 1) the aligned trial lie in the Euclidean space, which can be used by any Euclidean space signal processing and machine learning approach; 2) it can be computed very efficiently; and, 3) it does not need any labeled trials from the new subject. Experiments on motor imagery and event-related potentials demonstrated the effectiveness and efficiency of our approach.
The covariance matrices of EEG trials are SPD, and lie in a Riemannian space instead of a Euclidean space @cite_14 . Since the covariance matrices directly encode the spatial information of the EEG trials, and by appropriately augmenting the EEG trials (such as in ERP classification) they can also encode the temporal information, we can perform EEG classification directly based on the covariance matrices. This section introduces the MDRM classifier, which assigns a trial to the class whose Riemannian mean is the closest to its covariance matrix, and also a Riemannian space covariance matrix alignment approach (RA).
@cite_14
2746829572 2144093206 1674203940 2771397675
Objective: This paper tackles the problem of transfer learning in the context of electroencephalogram (EEG)-based brain–computer interface (BCI) classification. In particular, the problems of cross-session and cross-subject classification are considered. These problems concern the ability to use data from previous sessions or from a database of past users to calibrate and initialize the classifier, allowing a calibration-less BCI mode of operation. Methods: Data are represented using spatial covariance matrices of the EEG signals, exploiting the recent successful techniques based on the Riemannian geometry of the manifold of symmetric positive definite (SPD) matrices. Cross-session and cross-subject classification can be difficult, due to the many changes intervening between sessions and between subjects, including physiological, environmental, as well as instrumental changes. Here, we propose to affine transform the covariance matrices of every session subject in order to center them with respect to a reference covariance matrix, making data from different sessions subjects comparable. Then, classification is performed both using a standard minimum distance to mean classifier, and through a probabilistic classifier recently developed in the literature, based on a density function (mixture of Riemannian Gaussian distributions) defined on the SPD manifold. Results: The improvements in terms of classification performances achieved by introducing the affine transformation are documented with the analysis of two BCI datasets. Conclusion and significance: Hence, we make, through the affine transformation proposed, data from different sessions and subject comparable, providing a significant improvement in the BCI transfer learning problem. We propose a novel discriminative learning approach to image set classification by modeling the image set with its natural second-order statistic, i.e. covariance matrix. Since nonsingular covariance matrices, a.k.a. symmetric positive definite (SPD) matrices, lie on a Riemannian manifold, classical learning algorithms cannot be directly utilized to classify points on the manifold. By exploring an efficient metric for the SPD matrices, i.e., Log-Euclidean Distance (LED), we derive a kernel function that explicitly maps the covariance matrix from the Riemannian manifold to a Euclidean space. With this explicit mapping, any learning method devoted to vector space can be exploited in either its linear or kernel formulation. Linear Discriminant Analysis (LDA) and Partial Least Squares (PLS) are considered in this paper for their feasibility for our specific problem. We further investigate the conventional linear subspace based set modeling technique and cast it in a unified framework with our covariance matrix based modeling. The proposed method is evaluated on two tasks: face recognition and object categorization. Extensive experimental results show not only the superiority of our method over state-of-the-art ones in both accuracy and efficiency, but also its stability to two real challenges: noisy set data and varying set size. Metric learning has been shown to be highly effective to improve the performance of nearest neighbor classification. In this paper, we address the problem of metric learning for Symmetric Positive Definite (SPD) matrices such as covariance matrices, which arise in many real-world applications. Naively using standard Mahalanobis metric learning methods under the Euclidean geometry for SPD matrices is not appropriate, because the difference of SPD matrices can be a non-SPD matrix and thus the obtained solution can be uninterpretable. To cope with this problem, we propose to use a properly parameterized LogEuclidean distance and optimize the metric with respect to kernel-target alignment, which is a supervised criterion for kernel learning. Then the resulting non-trivial optimization problem is solved by utilizing the Riemannian geometry. Finally, we experimentally demonstrate the usefulness of our LogEuclidean metric learning algorithm on real-world classification tasks for EEG signals and texture patches. Inter-subject variability between individuals poses a challenge in inter-subject brain signal analysis problems. A new algorithm for subject-selection based on clustering covariance matrices on a Riemannian manifold is proposed. After unsupervised selection of the subsets of relevant subjects, data in a cluster is mapped to a tangent space at the mean point of covariance matrices in that cluster and an SVM classifier on labeled data from relevant subjects is trained. Experiment on an EEG seizure database shows that the proposed method increases the accuracy over state-of-the-art from 86.83 to 89.84 and specificity from 87.38 to 89.64 while reducing the false positive rate hour from 0.8 hour to 0.77 hour.