Abstract
Properly measuring the complexity of time series is an important issue. The permutation entropy (PE) is a widely used as an effective complexity measurement algorithm, but it is not suitable for the complexity description of multi-dimensional data. In this paper, in order to better measure the complexity of multi-dimensional time series, we proposed a modified multivariable PE (MMPE) algorithm with principal component analysis (PCA) dimensionality reduction, which is a new multi-dimensional time series complexity measurement algorithm. The analysis results of different chaotic systems verify that MMPE is effective. Moreover, we applied it to the comlexity analysis of EEG data. It shows that the person during mental arithmetic task has higher complexity comparing with the state before mental arithmetic task. In addition, we also discussed the necessity of the PCA dimensionality reduction.
Highlights
The complexity measurement algorithms and their applications are the current research hotspots in the field of nonlinear signal processing
In order to measure the complexity of multi-dimensional time series, we proposed a modified multivariate permutation entropy
The simulation analysis results prove that modified multivariable PE (MMPE) is effective for the complexity measurement of continuous chaotic systems
Summary
The complexity measurement algorithms and their applications are the current research hotspots in the field of nonlinear signal processing. In order to measure the complexity of time series, many complexity algorithms were proposed, such as the approximate entropy (ApEn) [13], sample entropy (SampEn) [14], fuzzy entropy (FuzzyEn) [15], dispersion entropy (DE) [16] and permutation entropy (PE) [17]. In order to fully consider the multichannel characteristics of EEG signals, some researchers used multivariate algorithms and PCA dimensionality reduction [25,26]. Motivated by the above discussions, in this paper, we proposed a modified multivariate PE measure method to analyze EEG signals with 21 channels, where PCA is employed to shrink the dimension of the data. We summarize this article and indicate the future work
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