The Comparative Study Of Blockwise Causality

In neuroscience, currently multi-channels of EEG recording and functionalimaging play a more and more important role in studying network mechanisms forcognition and disease diagnosis. The researchers not only study the functions of thespecific brain areas, also focus on causal influence between different brain regions.Multivariate block-wise Granger causality (BGC) is used to reflect causalinteractions among blocks of multivariate time series. Especially, spectral BGC andconditional spectral BGC are used to disclose block-wise causal flow among differentbrain areas in variant frequencies. Based on the research of block-wise causality,analysis the characteristics of block-wise Granger causality and propose block-wisenew causality (BNC).This paper points out that any contribution to current block of time series shouldbe considered when introducing a block-wise causality method. Any causality methodviolating this guideline inevitably cannot reflect well the true causality for two blocksof variables. Due to the use of the partial information of the multivariate linearregression model, BGC in time domain may not necessarily disclose true causality.Due to the use of the transfer function or its inverse matrix and partial information ofthe multivariate linear regression model, both of spectral BGC and conditionalspectral BGC have shortcomings and/or limitations which may inevitably lead tomisinterpretation results.NC among single variables in time and frequency domains were extended toblock-wise case based on the Fresenius norm of matrix and proposed BNC andspectral BNC. By using a concept of proportion, BNC describes how much proportionthat one block of variables occupies among all contributions to another block ofvariables, and used all information of the multivariate linear regression model.Multivariate linear regression models are used to compare BNC with BGC,spectral BNC with conditional spectral BGC. The results show that BNC wasconsistent with the true causality, and revealed the trend of true causality.At last, event-related potential (ERP) causality is analyzed for EEG data from anepilepsy patient and the results demonstrate that both of BGC and BNC methodsshow significant causality flow in frequency domain, but the spectral BNC methodyields satisfactory and convincing results which are consistent with event-relatedtime-frequency power spectrum activity.