Short-time multidimensional directed coherence for EEG Analysis

Abstract

This paper introduces the analysis of multivariate time series using multidimensional directed coherence (MDC) and multidimensional directed phase (MDP). Since there has been no study on nonstationary time series, we apply MDC and MDP to such time series using a short-time analyzing window. In this paper, we deal with an artificial multivariate time series, similar to an electroencephalogram (EEG), for numerical simulation. First, MDC and MDP are defined. Next, the artificial time series is analyzed using these methods. Finally, we consider whether these methods can be applied to nonstationary or weakly stationary time series. The production model for the artificial time series contains four characteristic structures: information flow rises, information flow dissolves, delay time of information flow varies, and center frequency of a source signal varies. As a result, the information flow in a multivariate artificial time series can be visualized by using MDC and MDP with a short-time analyzing window. 

Fast multidimensional directed information analysis

“…In contrast, some methods are suited for causality analysis, such as directed coherence analysis [1][2][3][4], innovation analysis [5], directed information analysis [6,7], Kaminski and Blinowska's method [8], and partial directed coherence [9,10]. We also developed multidimensional directed coherence analysis [11,12] and multidimensional directed phase analysis [13] as multidimensional signal processing methods for causality analysis. We proposed a method for the causality analysis of multidimensional time series based on the novel concept of multidimensional directed information (MDI) analysis.…”

“…Many EEG analyses by autoregressive model fitting have been carried out in the past [19][20][21][22][23][24][25]. Several studies [1][2][3][4][9][10][11][12][13] employed multivariate autoregressive model in the causality analysis of multichannel EEGs. We call the new calculation method 'fast multidimensional directed information analysis' (fast MDI analysis).…”