Classification of BCI-EEG based on augmented covariance matrix

Abstract

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.

Electroencephalography Signal Processing: A Comprehensive Review and Analysis of Methods and Techniques

“…The accuracy of performance measurement reached 85.36%, indicating that the proposed system outperformed the conventional machine learning EEG recognition classifier. In [135], they expanded the use of BCI to include motor imagery and presented a framework that used augmented covariance extracted from an autoregressive model for classification purposes. 4).…”

Pseudo-online framework for BCI evaluation: a MOABB perspective using various MI and SSVEP datasets

“…The numerous results performed on different datasets with different classification tasks, both binary and multi-class, showed a good alignment with state-of-the-art results. Overall, the method that shows the best performance is the augmented covariance method with classification using SVM on the tangent space [30]. However, one drawback of the augmented covariance method depends on the selection of two hyper parameters with a grid search which is computationally intensive due to the increasing size of the augmented covariance matrix with the order parameter [43].…”