Brain-computer interfaces (BCIs), which control external equipment using cerebral activity, have received considerable attention recently. Translating brain activities measured by electroencephalography (EEG) into correct control commands is a critical problem in this field. Most existing EEG decoding methods separate feature extraction from classification and thus are not robust across different BCI users. In this paper, we propose to learn subject-specific features jointly with the classification rule. We develop a deep convolutional network (ConvNet) to decode EEG signals end-to-end by stacking time-frequency transformation, spatial filtering, and classification together. Our proposed ConvNet implements a joint space-time-frequency feature extraction scheme for EEG decoding. Morlet wavelet-like kernels used in our network significantly reduce the number of parameters compared with classical convolutional kernels and endow the features learned at the corresponding layer with a clear interpretation, i.e. spectral amplitude. We further utilize subject-to-subject weight transfer, which uses parameters of the networks trained for existing subjects to initialize the network for a new subject, to solve the dilemma between a large number of demanded data for training deep ConvNets and small labeled data collected in BCIs. The proposed approach is evaluated on three public data sets, obtaining superior classification performance compared with the state-of-the-art methods.

The brain–computer interface (BCI), which provides a new way for humans to directly communicate with robots without the involvement of the peripheral nervous system, has recently attracted much attention. Among all the BCI paradigms, BCIs based on steady-state visual evoked potentials (SSVEPs) have the highest information transfer rate (ITR) and the shortest training time. Meanwhile, deep learning has provided an effective and feasible solution for solving complex classification problems in many fields, and many researchers have started to apply deep learning to classify SSVEP signals. However, the designs of deep learning models vary drastically. There are many hyper-parameters that influence the performance of the model in an unpredictable way. This study surveyed 31 deep learning models (2011–2023) that were used to classify SSVEP signals and analyzed their design aspects including model input, model structure, performance measure, etc. Most of the studies that were surveyed in this paper were published in 2021 and 2022. This survey is an up-to-date design guide for researchers who are interested in using deep learning models to classify SSVEP signals.

Learning vector quantization (LVQ) is a simple and efficient classification method, enjoying great popularity. However, in many classification scenarios, such as electroencephalogram (EEG) classification, the input features are represented by symmetric positive-definite (SPD) matrices that live in a curved manifold rather than vectors that live in the flat Euclidean space. In this article, we propose a new classification method for data points that live in the curved Riemannian manifolds in the framework of LVQ. The proposed method alters generalized LVQ (GLVQ) with the Euclidean distance to the one operating under the appropriate Riemannian metric. We instantiate the proposed method for the Riemannian manifold of SPD matrices equipped with the Riemannian natural metric. Empirical investigations on synthetic data and real-world motor imagery EEG data demonstrate that the performance of the proposed generalized learning Riemannian space quantization can significantly outperform the Euclidean GLVQ, generalized relevance LVQ (GRLVQ), and generalized matrix LVQ (GMLVQ). The proposed method also shows competitive performance to the state-of-the-art methods on the EEG classification of motor imagery tasks.

In many classification scenarios, the data to be analyzed can be naturally represented as points living on the curved Riemannian manifold of symmetric positive-definite (SPD) matrices. Due to its non-Euclidean geometry, usual Euclidean learning algorithms may deliver poor performance on such data. We propose a principled reformulation of the successful Euclidean generalized learning vector quantization (GLVQ) methodology to deal with such data, accounting for the nonlinear Riemannian geometry of the manifold through log-Euclidean metric (LEM). We first generalize GLVQ to the manifold of SPD matrices by exploiting the LEM-induced geodesic distance (GLVQ-LEM). We then extend GLVQ-LEM with metric learning. In particular, we study both 1) a more straightforward implementation of the metric learning idea by adapting metric in the space of vectorized log-transformed SPD matrices and 2) the full formulation of metric learning without matrix vectorization, thus preserving the second-order tensor structure. To obtain the distance metric in the full LEM learning (LEML) approaches, two algorithms are proposed. One method is to restrict the distance metric to be full rank, treating the distance metric tensor as an SPD matrix, and readily use the LEM framework (GLVQ-LEML-LEM). The other method is to cast no such restriction, treating the distance metric tensor as a fixed rank positive semidefinite matrix living on a quotient manifold with total space equipped with flat geometry (GLVQ-LEML-FM). Experiments on multiple datasets of different natures demonstrate the good performance of the proposed methods.

In this paper, we develop a new classification method for manifold-valued data in the framework of probabilistic learning vector quantization. In many classification scenarios, the data can be naturally represented by symmetric positive definite matrices, which are inherently points that live on a curved Riemannian manifold. Due to the non-Euclidean geometry of Riemannian manifolds, traditional Euclidean machine learning algorithms yield poor results on such data. In this paper, we generalize the probabilistic learning vector quantization algorithm for data points living on the manifold of symmetric positive definite matrices equipped with Riemannian natural metric (affine-invariant metric). By exploiting the induced Riemannian distance, we derive the probabilistic learning Riemannian space quantization algorithm, obtaining the learning rule through Riemannian gradient descent. Empirical investigations on synthetic data, image data , and motor imagery electroencephalogram (EEG) data demonstrate the superior performance of the proposed method.