Modified multiscale sample entropy and cross-sample entropy based on horizontal visibility graph

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As a crucial method of the feature extraction, the complexity measurement has a wide range of applications in the field of nonlinear time series research. This paper presents an innovative multiscale sample entropy for measuring the complexity of time series based on the horizontal visibility graph. The modified multiscale sample entropy has been proven to be robust on two artificial time series, and is capable of reducing the undefined entropy generated as a result of the increase in scale. We apply the modified multiscale sample entropy to the diagnosis of epilepsy. Using a novel data processing algorithm that combines frequency bands with decomposition, feature vectors are constructed for Electroencephalography (EEG) signals through the proposed entropy calculation algorithm, and different classes of subjects are categorized based on K-Nearest Neighbors, Support Vector Machine, and Artificial Neural Network. In the meantime, we propose an improved horizontal visibility graph-based multiscale cross-sample entropy method to measure the synchronization between two time series. It shows robustness in artificial data and decreases the appearance of undefined entropy to a certain extent. It is possible to extract the characteristics of sleep EEG signals and divide the subjects’ sleep stages using this method. Furthermore, this paper introduces the surrogate data test and the proposed methods have the ability to detect the nonlinearity and synchronization in simulations and in real-world experiments. Experimental results demonstrate that the two proposed frameworks are effective in monitoring human health and in assessing physical status through EEG signals.