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

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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.