Uehara Takashi, Sartori Matteo, Tanaka Toshihisa, Fiori Simone
Department of Electrical and Electronic Engineering, Tokyo University of Agriculture and Technology, Tokyo 184-8588, Japan.
School of Information and Automation Engineering, Università Politecnica delle Marche, Ancona 1-60131, Italy.
Neural Comput. 2017 Jun;29(6):1631-1666. doi: 10.1162/NECO_a_00963. Epub 2017 Apr 14.
The estimation of covariance matrices is of prime importance to analyze the distribution of multivariate signals. In motor imagery-based brain-computer interfaces (MI-BCI), covariance matrices play a central role in the extraction of features from recorded electroencephalograms (EEGs); therefore, correctly estimating covariance is crucial for EEG classification. This letter discusses algorithms to average sample covariance matrices (SCMs) for the selection of the reference matrix in tangent space mapping (TSM)-based MI-BCI. Tangent space mapping is a powerful method of feature extraction and strongly depends on the selection of a reference covariance matrix. In general, the observed signals may include outliers; therefore, taking the geometric mean of SCMs as the reference matrix may not be the best choice. In order to deal with the effects of outliers, robust estimators have to be used. In particular, we discuss and test the use of geometric medians and trimmed averages (defined on the basis of several metrics) as robust estimators. The main idea behind trimmed averages is to eliminate data that exhibit the largest distance from the average covariance calculated on the basis of all available data. The results of the experiments show that while the geometric medians show little differences from conventional methods in terms of classification accuracy in the classification of electroencephalographic recordings, the trimmed averages show significant improvement for all subjects.
协方差矩阵的估计对于分析多元信号的分布至关重要。在基于运动想象的脑机接口（MI-BCI）中，协方差矩阵在从记录的脑电图（EEG）中提取特征方面起着核心作用；因此，正确估计协方差对于EEG分类至关重要。本文讨论了在基于切空间映射（TSM）的MI-BCI中对样本协方差矩阵（SCM）进行平均以选择参考矩阵的算法。切空间映射是一种强大的特征提取方法，并且强烈依赖于参考协方差矩阵的选择。一般来说，观测信号可能包含异常值；因此，将SCM的几何平均值作为参考矩阵可能不是最佳选择。为了处理异常值的影响，必须使用稳健估计器。特别是，我们讨论并测试了使用几何中位数和截尾平均值（基于几种度量定义）作为稳健估计器。截尾平均值背后的主要思想是消除与基于所有可用数据计算出的平均协方差距离最大的数据。实验结果表明，虽然在脑电图记录分类的分类准确率方面，几何中位数与传统方法相比差异不大，但截尾平均值对所有受试者都有显著提高。
