New methods for analyzing high-dimensional results of connectivity examinations of the brain

提出了新的处理概念，用于分析大脑连接检查的高维结果。这些检验是通过时变部分定向相干（PDC）进行的。考虑以下三类方法。(1)时变PDC研究结果具有高维数据结构，因此进一步的分析必须包含降维。由于这样的数据结构可以看作一个张量，因此可以通过张量分解进行进一步的处理。因此，设想了包括张量分解在内的处理概念。这将导致PDC结果的重组。这些概念旨在改进时变连通性变化的分析。(2)对于确定的频带，时变PDC结果可以看作是一个图序列。图序列的分析方法应该是将图序列分解成相应的诱导子图集。这些方法的使用将提高对相关网络区域拓扑变化的分析。(3)为了尽量减少数据丢失（电极失效）对分析结果的影响，必须发展张量分解和图理论分析的归算概念。新方法将用于基于脑电图数据的连通性研究。这项研究的目的是客观的治疗儿童阅读障碍的成功。

New processing concepts for analyzing high-dimensional results of connectivity examinations of the brain are proposed.These examinations are carried out by using time-variant partial directed coherence (PDC). The following three classes of methods are considered.(1) Time-variant PDC studies lead to results with a high-dimensional data structure, consequently further analysis must include a dimensionality reduction. As such a data structure can be regarded as a tensor, further processing can be performed by tensor decomposition. Thus, processing concepts are envisaged which include tensor decomposition. This leads to a restructuring of the PDC results. Such concepts aim at an improvement of the analysis of time-variant connectivity changes.(2) For a defined frequency band time-variant PDC results can be regarded as a sequence of graphs. Methods should be developed for analysis of graph sequences which incorporate their decomposition into corresponding sets of induced sub-graphs.The use of these methods will improve the analysis of the topological changes of relevant network regions. (3) To minimize the impact of the loss of data (failure of electrodes) on the analysis results, imputation concepts for both tensor decomposition and graph-theoretical analysis must be developed.The new methods will be used for a connectivity study which is based on EEG data. The study aims to objectify the therapeutic success in children with dyslexia.