Electroencephalographic Data Analysis With Visibility Graph Technique for Quantitative Assessment of Brain Dysfunction

Usual techniques for electroencephalographic (EEG) data analysis lack some of the important properties essential for quantitative assessment of the progress of the dysfunction of the human brain. EEG data are essentially nonlinear and this nonlinear time series has been identified as multi-fractal in nature. We need rigorous techniques for such analysis. In this article, we present the visibility graph as the latest, rigorous technique that can assess the degree of multifractality accurately and reliably. Moreover, it has also been found that this technique can give reliable results with test data of comparatively short length. In this work, the visibility graph algorithm has been used for mapping a time series-EEG signals-to a graph to study complexity and fractality of the time series through investigation of its complexity. The power of scale-freeness of visibility graph has been used as an effective method for measuring fractality in the EEG signal. The scale-freeness of the visibility graph has also been observed after averaging the statistically independent samples of the signal. Scale-freeness of the visibility graph has been calculated for 5 sets of EEG data patterns varying from normal eye closed to epileptic. The change in the values is analyzed further, and it has been observed that it reduces uniformly from normal eye closed to epileptic.