Multiscale recurrence analysis of long-term nonlinear and nonstationary time series

Recurrence analysis is an effective tool to characterize and quantify the dynamics of complex systems, e.g., laminar, divergent or nonlinear transition behaviors. However, recurrence computation is highly expensive as the size of time series increases. Few, if any, previous approaches have been capable of quantifying the recurrence properties from a long-term time series, while which is often collected in the real-time monitoring of complex systems. This paper presents a novel multiscale framework to explore recurrence dynamics in complex systems and resolve computational issues for a large-scale dataset. As opposed to the traditional single-scale recurrence analysis, we characterize and quantify recurrence dynamics in multiple wavelet scales, which captures not only nonlinear but also nonstationary behaviors in a long-term time series. The proposed multiscale recurrence approach was utilized to identify heart failure subjects from the 24-h time series of heart rate variability (HRV). It was shown to identify the conditions of congestive heart failure with an average sensitivity of 92.1% and specificity of 94.7%. The proposed multiscale recurrence framework can be potentially extended to other nonlinear dynamic methods that are computationally expensive for large-scale datasets.