利用块Toeplitz增广协方差矩阵和Siegel度量提升运动想象BCI分类的计算效率
Enhancing Computational Efficiency of Motor Imagery BCI Classification with Block-Toeplitz Augmented Covariance Matrices and Siegel Metric
AI总结：
本文提出利用块Toeplitz增广协方差矩阵的数学结构并结合Siegel度量，在保持与ACM相似分类性能的同时显著提升运动想象BCI的计算效率，使其更适用于实时实验。
摘要：
脑电信号被表示为多维数据集。我们引入了对增广协方差方法（ACM）的增强，更充分地利用其数学性质，以改进运动想象分类。标准ACM是动力系统相空间重构与黎曼几何的结合。它基于构建对称正定（SPD）矩阵来提升分类。但该矩阵也具有此前被忽略的块Toeplitz结构。本工作在它们所属的真实流形（即块Toeplitz SPD矩阵集合）中处理此类矩阵。经过一些处理，该集合可被视为SPD流形与Siegel圆盘空间的乘积。所提方法使用MOABB框架进行了会话内评估测试。它实现了与ACM相似的分类性能，通常优于或至少不亚于最先进方法。同时，它显著提升了相比ACM的计算效率，使其更适合实时实验。
英文摘要：
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.
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