Anwendung trilinearer Komponentenanalyse auf die Analyse ereignisbezogener EEG-Potentiale

在头皮上记录的事件相关脑电图电位（ERPs）由几个重叠的成分组成。为了估计这些成分的参数，主成分分析（PCA）被推荐为25年前的选择方法。然而，如果不施加额外的约束，PCA不能得到唯一的数据分解（PCA的兄弟ICA也不能）。这些约束通常是形式化的（不是模型驱动的），例如，某些组件应该集中在尽可能少的变量上（Varimax和Promax旋转），这并不一定会导致在生理方面有意义的分解。Möcks （1988a, 1988b, 1991）建议该模型认为，一个成分的特征应该是其在各个观测点之间的地形分布是相同的。他证明了这将导致独特的模型驱动的解决方案，并开发了一种达到收敛的算法。本文首次将三线性成分分析系统地应用于ERP分析。为了达到这个目标，必须测试当前算法的数学核心，并且必须实现替代算法选项。应用程序的关键测试将在已有的数据集中实现，该数据集具有很大的实验方差，我们将在81-82任务中寻找由82引起的P3分量与前CNV的下行超调重叠多少的问题的答案。

As recorded at the scalp, event-related EEG potentials (ERPs) consist of several overlapping components. To estimate parameters of these components, Principal Component Analysis (PCA) was recommended as the method of choice 25 years ago. However, PCA cannot arrive at a unique decomposition of the data without imposing additional constraints (nor can PCA s younger sibling , ICA). These constraints are usually formal (not model-driven), e.g., that some component should be focused on as few variables as possible (Varimax and Promax rotations), which does not necessarily lead to a decomposition that makes sense in physiological terms. Möcks (1988a, 1988b, 1991) suggested the model that a component should be characterized by its topographical distribution across recording sites being identical across observations. He proved that this leads to unique model-driven solutions and he developed an algorithm that reaches convergence. This Trilinear Components Analysis will here be applied to ERP analysis systematically for the first time. To reach this goal, the mathematical core of the present algorithm has to be tested, and alternative algorithmic options have to be realized. The critical test for application will be realized in an already available data set that has large experimental variance where we will look for an answer on the question how much the P3 component evoked by 82 In an 81-82 task overlaps with the downswinging overshoot ofthe preceding CNV.