Utilizing embedding and decomposition for permutation entropy from multichannel signals

Traditional complexity measurement commonly emphasizes pattern structure and density estimation. Although the emergence of patterns inherently stems from the intrinsic autocorrelation and inter-correlations within signals, complexity measurements do not specifically cope with these correlations, leading to limited performance on multivariate time series. To address this limitation, we introduce time-delay embedding and singular value decomposition to permutation entropy (denoted as HES), which comprehensively characterizes the complexity of multichannel signals from multiple perspectives while reducing the impact of correlations. Our method achieves improved classification accuracy compared to state-of-the-art complexity metrics, and exhibits enhanced sensitivity to intrinsic mode memory changes. Furthermore, we combine HES with random forest or support vector machine classifiers and a surrogate optimization algorithm on three benchmark datasets. This combination method achieves higher accuracy which smoothly varies with embedding parameters. Moreover, HES excels in binary classification problem and is highly effective for short vibration signals.