Supplementary Material for “EEG Signal Processing in MI-BCI Applications with Improved Covariance Matrix Estimators”
This material is associated with the PhD Thesis of Javier Olias (which is supervised by Sergio Cruces) and the article:
“EEG Signal Processing in MI-BCI Applications with Improved Covariance Matrix Estimators” by J.Olias, R. Martin-Clemente, M.A. Sarmiento-Vega and S. Cruces,
which was accepted in 2019 by IEEE Transactions on Neural Systems and Rehabilitation Engineering.
In Supplementary.zip you will find the following files: 1) Data.mat Synthetic dataset of simulated EEG filtered recordings. It can be replaced by the datasets of the BCI competions for real testing. The data is stored in a MatLab struct type with the following fields: -x: Simulated EEG trials of dimension (n. samples)x(n. sensors)x(n. trials). -y: Classes of the trials in a vector of dimension (n. trials) x 1. -TrueCovClass: Tensor that stores the covariance of the 2 classes. Its dimension is (n. sensors)x(n. sensors) x 2
2) Demo.py Python demo file that illustrates the improvements obtained with the proposed power-normalization of the trials contained in Data.mat. The proposal can be interpreted as a generalization of Tyler's method for multiclass samples. The demo shows the improvement in the scale-invariant Riemannian distance of the estimated covariance matrices of the classes with respect to their true values once the proposed normalization is applied. > The average distance before normalization is 2.84 > The average distance after normalization is 1.88 It also reports the accuracy of the classification results obtained with the CSP+LDA classifier and the CSP+Tangent Space Logistic Regression classifiers, with and without normalization. The normalized versions nCSP+LDA and nCSP+TSLR clearly outperform the unnormalized ones CSP+LDA and CSP+TSLR. Accuracy CSP nCSP LDA 0.8175 0.8475 TSLR 0.8025 0.8700 3) Normalization_functions.py Stores the functions implementing the proposed normalization and the scale-invariant Riemannian distance. 4) Auxiliary_functions.py
Auxiliary functions for the demo. 5) Suplementary.pdf Supplementary material of the main article with extra figures and tables. It presents the obtained results of the algorithms for the multi-class paradigm.
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