Abstract
•Visible and non-visible motifs extracted from HVG provide a useful tool to measure the temporal asymmetry of a time series.•Motifs with different structural patterns can have the same visibility level.•The TIVM is an effective tool for discriminating healthy young, elderly and pathological groups.•The presence of small percentage of high amplitude outliers does not affect the performance of TIVM.
The time irreversibility is a characteristic feature of biological systems and its presence in heart rate (HR) is due to the complex dynamical process involved in the controlling mechanism of cardiovascular system (CVS). In this study, we propose a novel method referred to time irreversibility using visibility motifs (TIVM) for quantifying temporal asymmetry by extracting visible and non-visible horizontal visibility graph (HVG) motifs from a time series. The method can be applied using two simple approaches for transforming original time series into visible and non-visible motifs without mapping the time series into complex networks. Kullback-Leibler divergence (KLD) is used to quantify the temporal asymmetry between visible and non-visible HVG motifs of a time series. First, we explore the structural relation between HVG motifs and ordinal patterns reveal that motifs with different structures can have the similar visibility level. Next, we apply the method to find the asymmetry in different synthetic signals and real world interbeat interval (IBI) time series from healthy and pathological subjects. The findings reveal that the proposed method provide more accurate information about the healthy biological systems and changes occurring due to aging or disease. It is an effective tool for discriminating healthy young, elderly and pathological groups.