Multiscale Increment Entropy: An approach for quantifying the physiological complexity of biomedical time series

Time series data recorded from physiological systems often innately exhibit inherent physiological complexity variation on a long-range temporal scale. Multiscale analysis is considered vital for characterising the features of physiological signals. In this research, we propose a novel multiscale analysis method called multiscale increment entropy (MIE), which integrates incremental entropy (IncrEn) and multiscale analysis. MIE inherits the nature of IncrEn, which considers the fluctuation directions and amplitude of a time series. Experiments on both synthetic and real-world signals indicate that MIE performs better than popular approaches as a complexity index. On each temporal scale, MIE corroborates the complexity-loss theory of ageing and disease well. Furthermore, it reliably discriminates either between the EEG time series and heartbeat intervals of healthy subjects and patients or between the oxygen saturation variability of young and elderly, while commonly used algorithms do not perform well in the above cases. MIE requires less computational time compared to several popular approaches. It also has lower variations and is always defined across scales, even for short time series. These merits make it suitable for analysing unknown physiological time series.