Refined Weighted-Permutation Entropy: A Complexity Measure for Human Gait and Physiologic Signals with Outliers and Noise

The complexity quantification of human gait and physiologic signals has received considerable interest for wearable healthcare. Permutation entropy is one of the most prevalent algorithms for measuring the complexity of time series, but it fails to account for amplitude information with outliers and noise in such time series. Though weighted-permutation entropy aims to incorporate amplitude information by counterweighing the motif with its variance, it mixes noise and outliers with abrupt changes, which have a negative effect on the analysis result. To overcome this problem, this chapter proposes a refined weighted-permutation entropy by assigning fewer weights to outliers and more weights to regular spiky patterns according to the normal distribution function. The refined weighted-permutation entropy is used to analyze simulated synthetic signals with noise and outliers. The comparative analyses with the permutation entropy and weighted-permutation entropy are also performed. Moreover, human gait and ECG experimental data are analyzed by the proposed method. The results demonstrate its better robustness and stability than traditional methods in distinguishing different states of human gait and physiologic signals.