A novel encoding Lempel–Ziv complexity algorithm for quantifying the irregularity of physiological time series

Abstract

Background and objectiveThe Lempel–Ziv (LZ) complexity and its variants have been extensively used to analyze the irregularity of physiological time series. To date, these measures cannot explicitly discern between the irregularity and the chaotic characteristics of physiological time series. Our study compared the performance of an encoding LZ (ELZ) complexity algorithm, a novel variant of the LZ complexity algorithm, with those of the classic LZ (CLZ) and multistate LZ (MLZ) complexity algorithms. Methods and resultsSimulation experiments on Gaussian noise, logistic chaotic, and periodic time series showed that only the ELZ algorithm monotonically declined with the reduction in irregularity in time series, whereas the CLZ and MLZ approaches yielded overlapped values for chaotic time series and time series mixed with Gaussian noise, demonstrating the accuracy of the proposed ELZ algorithm in capturing the irregularity, rather than the complexity, of physiological time series. In addition, the effect of sequence length on the ELZ algorithm was more stable compared with those on CLZ and MLZ, especially when the sequence length was longer than 300. A sensitivity analysis for all three LZ algorithms revealed that both the MLZ and the ELZ algorithms could respond to the change in time sequences, whereas the CLZ approach could not. Cardiac interbeat (RR) interval time series from the MIT-BIH database were also evaluated, and the results showed that the ELZ algorithm could accurately measure the inherent irregularity of the RR interval time series, as indicated by lower LZ values yielded from a congestive heart failure group versus those yielded from a normal sinus rhythm group (p < 0.01).