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

提出了一种新的处理概念，用于分析大脑连通性检查的高维结果，这些检查是通过使用时变部分有向相干（PDC）来进行的。考虑以下三类方法。（一） 时变PDC的研究导致的结果与高维数据结构，因此，进一步的分析必须包括降维。由于这种数据结构可以被视为张量，因此可以通过张量分解来执行进一步的处理。因此，设想包括张量分解的处理概念。这导致了PDC结果的重组。这些概念旨在改进时变连通性变化的分析。（二） 对于定义的频带，时变PDC结果可以被视为一系列图形。应发展将图序列分解为相应的导出子图集的图序列分析方法，这些方法的使用将改进对相关网络区域的拓扑变化的分析。（三） 为了最大限度地减少数据丢失（电极故障）对分析结果的影响，必须开发张量分解和图论分析的插补概念。新方法将用于基于脑电数据的连通性研究。这项研究的目的是客观的治疗成功的儿童阅读障碍。

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.