The integration of Deep Learning (DL) algorithms on brain signal analysis is still in its nascent stages compared to their success in fields like Computer Vision, especially in Brain-Computer Interface (BCI), where the brain activity is decoded to control external devices without requiring muscle control. Electroencephalography (EEG) is a widely adopted choice for designing BCI systems due to its non-invasive and cost-effective nature and excellent temporal resolution. Still, it comes at the expense of limited training data, poor signal-to-noise, and a large variability across and within-subject recordings. Finally, setting up a BCI system with many electrodes takes a long time, hindering the widespread adoption of reliable DL architectures in BCIs outside research laboratories. To improve adoption, we need to improve user comfort using, for instance, reliable algorithms that operate with few electrodes. Approach: Our research aims to develop a DL algorithm that delivers effective results with a limited number of electrodes. Taking advantage of the Augmented Covariance Method with SPDNet, we propose the SPDNet$_{\psi}$ architecture and analyze its performance and computational impact, as well as the interpretability of the results. The evaluation is conducted on 5-fold cross-validation, using only three electrodes positioned above the Motor Cortex. The methodology was tested on nearly 100 subjects from several open-source datasets using the Mother Of All BCI Benchmark (MOABB) framework. Main results: The results of our SPDNet$_{\psi}$ demonstrate that the augmented approach combined with the SPDNet significantly outperforms all the current state-of-the-art DL architecture in MI decoding. Significance: This new architecture is explainable, with a low number of trainable parameters and a reduced carbon footprint.

Electroencephalographic signals are represented as multidimensional datasets. We introduce an enhancement to the augmented covariance method (ACM), exploiting more thoroughly its mathematical properties, in order to improve motor imagery classification.Standard ACM emerges as a combination of phase space reconstruction of dynamical systems and of Riemannian geometry. Indeed, it is based on the construction of a Symmetric Positive Definite matrix to improve classification. But this matrix also has a Block-Toeplitz structure that was previously ignored. This work treats such matrices in the real manifold to which they belong: the set of Block-Toeplitz SPD matrices. After some manipulation, this set is can be seen as the product of an SPD manifold and a Siegel Disk Space.The proposed methodology was tested using the MOABB framework with a within-session evaluation procedure. It achieves a similar classification performance to ACM, which is typically better than -- or at worse comparable to -- state-of-the-art methods. But, it also improves consequently the computational efficiency over ACM, making it even more suitable for real time experiments.

Objective. This study conduct an extensive Brain-computer interfaces (BCI) reproducibility analysis on open electroencephalography datasets, aiming to assess existing solutions and establish open and reproducible benchmarks for effective comparison within the field. The need for such benchmark lies in the rapid industrial progress that has given rise to undisclosed proprietary solutions. Furthermore, the scientific literature is dense, often featuring challenging-to-reproduce evaluations, making comparisons between existing approaches arduous. Approach. Within an open framework, 30 machine learning pipelines (separated into raw signal: 11, Riemannian: 13, deep learning: 6) are meticulously re-implemented and evaluated across 36 publicly available datasets, including motor imagery (14), P300 (15), and SSVEP (7). The analysis incorporates statistical meta-analysis techniques for results assessment, encompassing execution time and environmental impact considerations. Main results. The study yields principled and robust results applicable to various BCI paradigms, emphasizing motor imagery, P300, and SSVEP. Notably, Riemannian approaches utilizing spatial covariance matrices exhibit superior performance, underscoring the necessity for significant data volumes to achieve competitive outcomes with deep learning techniques. The comprehensive results are openly accessible, paving the way for future research to further enhance reproducibility in the BCI domain. Significance. The significance of this study lies in its contribution to establishing a rigorous and transparent benchmark for BCI research, offering insights into optimal methodologies and highlighting the importance of reproducibility in driving advancements within the field.

Objective: BCI (Brain-Computer Interface) technology operates in three modes: online, offline, and pseudo-online. In the online mode, real-time EEG data is constantly analyzed. In offline mode, the signal is acquired and processed afterwards. The pseudo-online mode processes collected data as if they were received in real-time. The main difference is that the offline mode often analyzes the whole data, while the online and pseudo-online modes only analyze data in short time windows. Offline analysis is usually done with asynchronous BCIs, which restricts analysis to predefined time windows. Asynchronous BCI, compatible with online and pseudo-online modes, allows flexible mental activity duration. Offline processing tends to be more accurate, while online analysis is better for therapeutic applications. Pseudo-online implementation approximates online processing without real-time constraints. Many BCI studies being offline introduce biases compared to real-life scenarios, impacting classification algorithm performance. Approach: The objective of this research paper is therefore to extend the current MOABB framework, operating in offline mode, so as to allow a comparison of different algorithms in a pseudo-online setting with the use of a technology based on overlapping sliding windows. To do this will require the introduction of a idle state event in the dataset that takes into account all different possibilities that are not task thinking. To validate the performance of the algorithms we will use the normalized Matthews Correlation Coefficient (nMCC) and the Information Transfer Rate (ITR). Main results: We analyzed the state-of-the-art algorithms of the last 15 years over several Motor Imagery (MI) datasets composed by several subjects, showing the differences between the two approaches from a statistical point of view. Significance: The ability to analyze the performance of different algorithms in offline and pseudo-online modes will allow the BCI community to obtain more accurate and comprehensive reports regarding the performance of classification algorithms.

Objective: Electroencephalography signals are recorded as a multidimensional dataset. We propose a new framework based on the augmented covariance extracted from an autoregressive model to improve motor imagery classification. Methods: From the autoregressive model can be derived the Yule-Walker equations, which show the emergence of a symmetric positive definite matrix: the augmented covariance matrix. The state-of the art for classifying covariance matrices is based on Riemannian Geometry. A fairly natural idea is therefore to extend the standard approach using these augmented covariance matrices. The methodology for creating the augmented covariance matrix shows a natural connection with the delay embedding theorem proposed by Takens for dynamical systems. Such an embedding method is based on the knowledge of two parameters: the delay and the embedding dimension, respectively related to the lag and the order of the autoregressive model. This approach provides new methods to compute the hyper-parameters in addition to standard grid search. Results: The augmented covariance matrix performed noticeably better than any state-of-the-art methods. We will test our approach on several datasets and several subjects using the MOABB framework, using both within-session and cross-session evaluation. Conclusion: The improvement in results is due to the fact that the augmented covariance matrix incorporates not only spatial but also temporal information, incorporating nonlinear components of the signal through an embedding procedure, which allows the leveraging of dynamical systems algorithms. Significance: These results extend the concepts and the results of the Riemannian distance based classification algorithm.