Electroencephalogram data used in the domain of brain–computer interfaces typically has subpar signal-to-noise ratio and data acquisition is expensive. An effective and commonly used classifier to discriminate event-related potentials is the linear discriminant analysis which, however, requires an estimate of the feature distribution. While this information is provided by the feature covariance matrix its large number of free parameters calls for regularization approaches like Ledoit–Wolf shrinkage. Assuming that the noise of event-related potential recordings is not time-locked, we propose to decouple the time component from the covariance matrix of event-related potential data in order to further improve the estimates of the covariance matrix for linear discriminant analysis. We compare three regularized variants thereof and a feature representation based on Riemannian geometry against our proposed novel linear discriminant analysis with time-decoupled covariance estimates. Extensive evaluations on 14 electroencephalogram datasets reveal, that the novel approach increases the classification performance by up to four percentage points for small training datasets, and gracefully converges to the performance of standard shrinkage-regularized LDA for large training datasets. Given these results, practitioners in this field should consider using our proposed time-decoupled covariance estimation when they apply linear discriminant analysis to classify event-related potentials, especially when few training data points are available.

用于脑机接口领域的脑电图数据通常具有低于标准的信噪比，并且数据采集成本高昂。一种有效且常用的区分事件相关电位的分类器是线性判别分析，然而，它需要对特征分布进行估计。虽然此信息由特征协方差矩阵提供，但其大量自由参数需要正则化方法，如 Ledoit-Wolf 收缩。假设事件相关电位记录的噪声不是时间锁定的，我们建议将时间分量与事件相关电位数据的协方差矩阵解耦，以进一步改进协方差矩阵的估计以进行线性判别分析。我们将其三个正则化变体和基于黎曼几何的特征表示与我们提出的具有时间解耦协方差估计的新型线性判别分析进行了比较。对 14 个脑电图数据集的广泛评估表明，新方法将小型训练数据集的分类性能提高了多达四个百分点，并优雅地收敛到大型训练数据集的标准收缩正则化 LDA 的性能。鉴于这些结果，该领域的从业者在应用线性判别分析对事件相关电位进行分类时，尤其是当可用的训练数据点很少时，应考虑使用我们提出的时间解耦协方差估计。