arXiv 2302.045082023-02-09cs.HCcs.LGphysics.data-anstat.ML

基于增广协方差矩阵的BCI-EEG分类

Classification of BCI-EEG based on augmented covariance matrix

Université Côte d’Azur (UCA)（蔚蓝海岸大学（UCA））；Centre Inria d’Université Côte d’Azur（蔚蓝海岸大学国家信息与自动化研究所中心）

Igor Carrara, Théodore Papadopoulo

摘要：

目的：将脑电信号记录为多维数据集。我们提出了一个新的框架的基础上增强协方差提取自回归模型，以提高运动想象分类。研究方法：从自回归模型可以推导出尤尔-沃克方程，它显示了一个对称正定矩阵的出现：增广协方差矩阵。对协方差矩阵进行分类的现有技术是基于黎曼几何。因此，一个相当自然的想法是使用这些增广协方差矩阵来扩展标准方法。创建增广协方差矩阵的方法与Takens为动力系统提出的延迟嵌入定理有着天然的联系。这样的嵌入方法是基于两个参数的知识：延迟和嵌入维数，分别与自回归模型的滞后和阶。这种方法提供了新的方法来计算超参数除了标准的网格搜索。结果：增广协方差矩阵的表现明显优于任何国家的最先进的方法。我们将使用MOABB框架在几个数据集和几个主题上测试我们的方法，使用会话内和跨会话评估。结论：结果的改善是由于这样的事实，即增强的协方差矩阵不仅包含空间信息，而且包含时间信息，通过嵌入过程，这允许利用动态系统算法的信号的非线性分量。意义：这些结果扩展了基于黎曼距离的分类算法的概念和结果。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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