Improved Permutation Entropy for Measuring Complexity of Time Series under Noisy Condition

Measuring complexity of observed time series plays an important role for understanding the characteristics of the system under study. Permutation entropy (PE) is a powerful tool for complexity analysis, but it has some limitations. For example, the amplitude information is discarded; the equalities (i.e., equal values in the analysed signal) are not properly dealt with; and the performance under noisy condition remains to be improved. In this paper, the improved permutation entropy (IPE) is proposed. The presented method combines some advantages of previous modifications of PE. Its effectiveness is validated through both synthetic and experimental analyses. Compared with PE, IPE is capable of detecting spiky features and correctly differentiating heart rate variability (HRV) signals. Moreover, it performs better under noisy condition. Ship classification experiment results demonstrate that IPE achieves 28.66% higher recognition rate than PE at 0dB. Hence, IPE could be used as an alternative of PE for analysing time series under noisy condition.