Surrogate Data Method Requires End-Matched Segmentation of Electroencephalographic Signals to Estimate Non-linearity

The aim of the study is to clarify the impact of the strong cyclic signal component on the results of surrogate data method in the case of resting electroencephalographic (EEG) signals. In addition, the impact of segment length is analyzed. Different non-linear measures (fractality, complexity, etc.) of neural signals have been demonstrated to be useful to infer the non-linearity of brain functioning from EEG. The surrogate data method is often applied to test whether or not the non-linear structure can be captured from the data. In addition, a growing number of studies are using surrogate data method to determine the statistical threshold of connectivity values in network analysis. Current study focuses on the conventional segmentation of EEG signals, which could lead to false results of surrogate data method. More specifically, the necessity to use end-matched segments that contain an integer number of dominant frequency periods is studied. EEG recordings from 80 healthy volunteers during eyes-closed resting state were analyzed using multivariate surrogate data method. The artificial surrogate data were generated by shuffling the phase spectra of original signals. The null hypothesis that time series were generated by a linear process was rejected by statistically comparing the non-linear statistics calculated for original and surrogate data sets. Five discriminating statistics were used as non-linear estimators: Higuchi fractal dimension (HFD), Katz fractal dimension (KFD), Lempel-Ziv complexity (LZC), sample entropy (SampEn) and synchronization likelihood (SL). The results indicate that the number of segments evaluated as non-linear differs in the case of various non-linear measures and changes with the segment length. The main conclusion is that the dependence on the deviation of the segment length from full periods of dominant EEG frequency has non-monotonic character and causes misleading results in the evaluation of non-linearity. Therefore, in the case of the signals with non-monotonic spectrum and strong dominant frequency, the correct use of surrogate data method requires the signal length comprising of full periods of the spectrum dominant frequency. The study is important to understand the influence of incorrect selection of EEG signal segment length for surrogate data method to estimate non-linearity.